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AuthorTitleYearJournal/ProceedingsReftypeDOI/URL
Eldén, L. Computing Frechet Derivatives in Partial Least Squares Regression

[Abstract] [BibTeX]

 2015 Linear Algebra and its Applications
Vol. 473, pp. 316-338 		 article DOI URL 
Abstract: Partial least squares is a common technique for multivariate regression. The pro- cedure is recursive and in each step basis vectors are computed for the explaining variables and the solution vectors. A linear model is fitted by projection onto the span of the basis vectors. The procedure is mathematically equivalent to Golub-Kahan bidiagonalization, which is a Krylov method, and which is equiv- alent to a pair of matrix factorizations. The vectors of regression coefficients and prediction are non-linear functions of the right hand side. An algorithm for computing the Frechet derivatives of these functions is derived, based on perturbation theory for the matrix factorizations. From the Frechet derivative of the prediction vector one can compute the number of degrees of freedom, which can be used as a stopping criterion for the recursion. A few numerical examples are given.
BibTeX: 
@article{eld15,
  author = {L. Eldén},
  title = {Computing Frechet Derivatives in Partial Least Squares Regression},
  journal = {Linear Algebra and its Applications},
  year = {2015},
  volume = {473},
  pages = {316-338},
  url = {http://www.sciencedirect.com/science/article/pii/S0024379514006028},
  doi = {http://dx.doi.org/10.1016/j.laa.2014.09.017}
}
Feng., X. and Eldén, L. Solving a Cauchy problem for a 3D elliptic PDE with variable coefficients by a quasi-boundary-value method

[Abstract] [BibTeX]

 2014 Inverse Problems
Vol. 30, pp. 015005 		 article DOI URL 
Abstract: An ill-posed Cauchy problem for a 3D elliptic partial differential equation with variable coefficients is considered. A well-posed quasi-boundary-value (QBV) problem is given to approximate it. Some stability estimates are given. For the numerical implementation, a large sparse system is obtained from discretizing the QBV problem using the finite difference method. A left-preconditioned generalized minimum residual method is used to solve the large system effectively. For the preconditioned system, a fast solver using the fast Fourier transform is given. Numerical results show that the method works well.
BibTeX: 
@article{feel14,
  author = {X. Feng. and L. Eldén},
  title = {Solving a Cauchy problem for a 3D elliptic PDE with variable coefficients by a quasi-boundary-value method},
  journal = {Inverse Problems},
  year = {2014},
  volume = {30},
  pages = {015005},
  url = {http://stacks.iop.org/0266-5611/30/i=1/a=015005},
  doi = {http://dx.doi.org/10.1088/0266-5611/30/1/015005}
}
Ranjbar, Z. and Eldén, L. Solving an Ill-Posed Cauchy Problem for a Two-Dimensional Parabolic PDE with Variable Coefficients Using a Preconditioned GMRES Method

[Abstract] [BibTeX]

 2014 SIAM Journal on Scientific Computing
Vol. 36(5), pp. B868-B886 		 article DOI URL 
Abstract: The sideways parabolic equation (SPE) is a model of the problem of determining the temperature on the surface of a body from the interior measurements. Mathematically it can be formulated as a noncharacteristic Cauchy problem for a parabolic partial differential equation. This problem is severely ill-posed in an L2 setting. We use a preconditioned generalized minimum residual method (GMRES) to solve a two-dimensional SPE with variable coefficients. The preconditioner is singular and chosen in a way that allows efficient implementation using the FFT. The preconditioner is a stabilized solver for a nearby problem with constant coefficients, and it reduces the number of iterations in the GMRES algorithm significantly. Numerical experiments are performed that demonstrate the performance of the proposed method.
BibTeX: 
@article{rael14,
  author = {Ranjbar, Z. and Eldén, L.},
  title = {Solving an Ill-Posed Cauchy Problem for a Two-Dimensional Parabolic PDE with Variable Coefficients Using a Preconditioned GMRES Method},
  journal = {SIAM Journal on Scientific Computing},
  year = {2014},
  volume = {36},
  number = {5},
  pages = {B868-B886},
  url = {http://dx.doi.org/10.1137/130951166},
  doi = {http://dx.doi.org/10.1137/130951166}
}
Rezghi, M., Hosseini, S.M. and Eldén, L. Best Kronecker Product Approximation of the Blurring Operator in Three Dimensional Image Restoration Problems

[BibTeX]

 2014 SIAM J. Matrix Anal. Appl.
Vol. 35(3), pp. 1086-1104 		 article DOI URL 
BibTeX: 
@article{rhe14,
  author = {M. Rezghi and S. M. Hosseini and L. Eldén},
  title = {Best Kronecker Product Approximation of the Blurring Operator in Three Dimensional Image Restoration Problems},
  journal = {SIAM J. Matrix Anal. Appl.},
  year = {2014},
  volume = {35},
  number = {3},
  pages = {1086-1104},
  url = {http://epubs.siam.org/toc/sjmael/35/3},
  doi = {http://dx.doi.org/10.1137/130917260}
}
Eldén, L., Merkel, M., Ahrenberg, L. and Fagerlund, M. Computing Semantic Clusters by Semantic Mirroring and Spectral Graph Partitioning

[Abstract] [BibTeX]

 2013 Mathematics in Computer Science
Vol. 7, pp. 293-313 		 article DOI  
Abstract: Using the technique of semantic mirroring a graph is obtained that represents words and their translations from a parallel corpus or a bilingual lexicon. The connectedness of the graph holds information about the semantic relations of words that occur in the translations. Spectral graph theory is used to partition the graph, which leads to a grouping of the words in different clusters. We illustrate the method using a small sample of seed words from a lexicon of Swedish and English adjectives and discuss its application to computational lexical semantics and lexicography.
BibTeX: 
@article{emaf13,
  author = {L. Eldén and M. Merkel and L. Ahrenberg and M. Fagerlund},
  title = {Computing Semantic Clusters by Semantic Mirroring and Spectral Graph Partitioning},
  journal = {Mathematics in Computer Science},
  year = {2013},
  volume = {7},
  pages = {293-313},
  doi = {http://dx.doi.org/10.1007/s11786-013-0159-4}
}
Savas, B. and Eldén, L. Krylov-type methods for tensor computations I

[Abstract] [BibTeX]

 2013 Linear Algebra and its Applications
Vol. 438(0), pp. 891-918 		 article DOI URL 
Abstract: Several Krylov-type procedures are introduced that generalize matrix Krylov methods for tensor computations. They are denoted minimal Krylov recursion, maximal Krylov recursion, and contracted tensor product Krylov recursion. It is proved that, for a given tensor A with multilinear rank-(p, q, r), the minimal Krylov recursion extracts the correct subspaces associated to the tensor in p+q+r number of tensor–vector–vector multiplications. An optimized minimal Krylov procedure is described that, for a given multilinear rank of an approximation, produces a better approximation than the standard minimal recursion. We further generalize the matrix Krylov decomposition to a tensor Krylov decomposition. The tensor Krylov methods are intended for the computation of low multilinear rank approximations of large and sparse tensors, but they are also useful for certain dense and structured tensors for computing their higher order singular value decompositions or obtaining starting points for the best low-rank computations of tensors. A set of numerical experiments, using real-world and synthetic data sets, illustrate some of the properties of the tensor Krylov methods.
BibTeX: 
@article{sael11,
  author = {Berkant Savas and Lars Eldén},
  title = {Krylov-type methods for tensor computations I},
  journal = {Linear Algebra and its Applications},
  year = {2013},
  volume = {438},
  number = {0},
  pages = {891-918},
  url = {http://www.sciencedirect.com/science/article/pii/S0024379511007877},
  doi = {http://dx.doi.org/10.1016/j.laa.2011.12.007}
}
Eldén, L. and Simoncini, V. Solving Ill-Posed Linear Systems with GMRES and a Singular Preconditioner

[BibTeX]

 2012 SIAM J. Matrix Anal. Appl.
Vol. 33, pp. 1369-1394 		 article DOI  
BibTeX: 
@article{elsi12,
  author = {L. Eldén and V. Simoncini},
  title = {Solving Ill-Posed Linear Systems with GMRES and a Singular Preconditioner},
  journal = {SIAM J. Matrix Anal. Appl.},
  year = {2012},
  volume = {33},
  pages = {1369-1394},
  doi = {http://dx.doi.org/10.1137/110832793}
}
Eldén, L. and Savas, B. Perturbation Theory and Optimality Conditions for the Best Multilinear Rank Approximation of a Tensor

[Abstract] [BibTeX]

 2011 SIAM J. Matrix Anal. Appl.,
Vol. 32, pp. 1422-1450 		 article DOI URL 
Abstract: The problem of computing the best rank-$(p,q,r)$ approximation of a third order tensor is considered. First the problem is reformulated as a maximization problem on a product of three Grassmann manifolds. Then expressions for the gradient and the Hessian are derived in a local coordinate system at a stationary point, and conditions for a local maximum are given. A first order perturbation analysis is performed using the Grassmann manifold framework. The analysis is illustrated in a few examples, and it is shown that the perturbation theory for the singular value decomposition is a special case of the tensor theory.
BibTeX: 
@article{elsa11,
  author = {L. Eldén and B. Savas},
  title = {Perturbation Theory and Optimality Conditions for the Best Multilinear Rank Approximation of a Tensor},
  journal = {SIAM J. Matrix Anal. Appl.,},
  year = {2011},
  volume = {32},
  pages = {1422-1450},
  url = {http://epubs.siam.org.lt.ltag.bibl.liu.se/sima/resource/1/sjmael/v32/i4/p1422_s1},
  doi = {http://dx.doi.org/10.1137/110823298}
}
Rezghi, M. and Eldén, L. Diagonalization of Tensors with Circulant Structure

[BibTeX]

 2011 Lin. Alg. Appl.
Vol. 435, pp. 422–447 		 article  
BibTeX: 
@article{reel11,
  author = {M. Rezghi and L. Eldén},
  title = {Diagonalization of Tensors with Circulant Structure},
  journal = {Lin. Alg. Appl.},
  year = {2011},
  volume = {435},
  pages = {422–447}
}
Feng, X.-L., Eldén, L. and Fu, C.-L. Stability and regularization of a backward parabolic PDE with variable coefficients

[BibTeX]

 2010 J. Inverse and Ill-Posed Problems
Vol. 18, pp. 217-243 		 article  
BibTeX: 
@article{fef10,
  author = {Xiao-Li Feng and Lars Eldén and Chu-Li Fu},
  title = {Stability and regularization of a backward parabolic PDE with variable coefficients},
  journal = {J. Inverse and Ill-Posed Problems},
  year = {2010},
  volume = {18},
  pages = {217-243}
}
Feng, X.-L., Eldén, L. and Fu, C.-L. A quasi-boundary-value method for the Cauchy problem for elliptic equations with nonhomogeneous Neumann data

[BibTeX]

 2010 J. Inv. Ill-Posed Problems
Vol. 18, pp. 617–645 		 article DOI URL 
BibTeX: 
@article{fef10a,
  author = {Xiao-Li Feng and Lars Eldén and Chu-Li Fu},
  title = {A quasi-boundary-value method for the Cauchy problem for elliptic equations with nonhomogeneous Neumann data},
  journal = {J. Inv. Ill-Posed Problems},
  year = {2010},
  volume = {18},
  pages = {617–645},
  url = {http://www.reference-global.com/doi/abs/10.1515/JIIP.2010.028},
  doi = {http://dx.doi.org/DOI 10.1515/ JIIP.2010.028}
}
Fagerlund, M., Merkel, M., Eldén, L. and Ahrenberg, L. Computing Word Senses by Semantic Mirroring and Spectral Graph Partitioning

[BibTeX]

 2010 Proceedings of TextGraphs-5 - 2010 Workshop on Graph-based Methods for Natural Language Processing, pp. 103-107  inproceedings URL 
BibTeX: 
@inproceedings{fmea10,
  author = {Fagerlund, Martin and Merkel, Magnus and Eldén, Lars and Ahrenberg, Lars},
  title = {Computing Word Senses by Semantic Mirroring and Spectral Graph Partitioning},
  booktitle = {Proceedings of TextGraphs-5 - 2010 Workshop on Graph-based Methods for Natural Language Processing},
  publisher = {Association for Computational Linguistics},
  year = {2010},
  pages = {103--107},
  url = {http://www.aclweb.org/anthology/W10-2317}
}
Simonsson, L. and Eldén, L. Grassmann algorithms for low rank approximation of matrices with missing values

[BibTeX]

 2010 BIT Numerical Mathematics
Vol. 50, pp. 173-191 		 article DOI  
BibTeX: 
@article{siel10a,
  author = {L. Simonsson and L. Eldén},
  title = {Grassmann algorithms for low rank approximation of matrices with missing values},
  journal = {BIT Numerical Mathematics},
  year = {2010},
  volume = {50},
  pages = {173-191},
  doi = {http://dx.doi.org/10.1007/s10543-010-0253-9}
}
Eldén, L. and Savas, B. A Newton--Grassmann method for computing the Best Multi-Linear Rank-($r_1,r_2,r_3$) Approximation of a Tensor

[Abstract] [BibTeX]

 2009 SIAM J. Matrix Anal. Appl.
Vol. 31, pp. 248-271 		 article  
Abstract: We derive a Newton method for computing the best rank-$(r_1,r_2,r_3)$ approximation of a given $J x K x L$ tensor $$. The problem is formulated as an approximation problem on a product of Grassmann manifolds. Incorporating the manifold structure into Newton's method ensures that all iterates generated by the algorithm are points on the Grassmann manifolds. We also introduce a consistent notation for matricizing a tensor, for contracted tensor products and some tensor-algebraic manipulations, which simplify the derivation of the Newton equations and enable straightforward algorithmic implementation. Experiments show a quadratic convergence rate for the Newton-Grassmann algorithm.
BibTeX: 
@article{elsa09,
  author = {L. Eldén and B. Savas},
  title = {A Newton--Grassmann method for computing the Best Multi-Linear Rank-($r_1,r_2,r_3$) Approximation of a Tensor},
  journal = {SIAM J. Matrix Anal. Appl.},
  year = {2009},
  volume = {31},
  pages = {248-271}
}
Eldén, L. and Simoncini, V. Numerical Solution of a Cauchy Problem for an Elliptic Equation by Krylov Subspaces

[BibTeX]

 2009 Inverse Probl.
Vol. 25(6), pp. 065002 		 article URL 
BibTeX: 
@article{elsi09,
  author = {L. Eldén and V. Simoncini},
  title = {Numerical Solution of a Cauchy Problem for an Elliptic Equation by Krylov Subspaces},
  journal = {Inverse Probl.},
  year = {2009},
  volume = {25},
  number = {6},
  pages = {065002},
  url = {http://stacks.iop.org/0266-5611/25/i=6/a=065002}
}
Bro, R. and Eldén, L. PLS works

[BibTeX]

 2008 J. Chemometrics
Vol. 23, pp. 69-71 		 article DOI  
BibTeX: 
@article{brel08,
  author = {R. Bro and L. Eldén},
  title = {PLS works},
  journal = {J. Chemometrics},
  year = {2008},
  volume = {23},
  pages = {69-71},
  doi = {http://dx.doi.org/10.1002/cem.1177}
}
Ranjbar, Z. and Eldén, L. Numerical Analysis of an Ill-Posed Cauchy Problem for a Convection-Diffusion Equation

[BibTeX]

 2007 Inverse Problems in Science and Engineering
Vol. 15(3), pp. 191-211 		 article  
BibTeX: 
@article{rael:05,
  author = {Z. Ranjbar and L. Eldén},
  title = {Numerical Analysis of an Ill-Posed Cauchy Problem for a Convection-Diffusion Equation},
  journal = {Inverse Problems in Science and Engineering},
  year = {2007},
  volume = {15},
  number = {3},
  pages = {191-211}
}
Savas, B. and Eldén, L. Handwritten Digit Classification using Higher Order Singular Value Decomposition

[BibTeX]

 2007 Pattern Recognition
Vol. 40, pp. 993-1003 		 article  
BibTeX: 
@article{sael:06,
  author = {B.~Savas and L. Eldén},
  title = {Handwritten Digit Classification using Higher Order Singular Value Decomposition},
  journal = {Pattern Recognition},
  year = {2007},
  volume = {40},
  pages = {993-1003}
}
Eldén, L. Numerical Linear Algebra in Data Mining

[BibTeX]

 2006 Acta Numerica
Vol. 15, pp. 327-384 		 article  
BibTeX: 
@article{eld:06,
  author = {L. Eldén},
  title = {Numerical Linear Algebra in Data Mining},
  journal = {Acta Numerica},
  year = {2006},
  volume = {15},
  pages = {327-384}
}
Eldén, L. and Berntsson, F. A stability estimate for a Cauchy problem for an elliptic partial differential equation

[BibTeX]

 2005 Inverse Problems
Vol. 21, pp. 1643-1653 		 article  
BibTeX: 
@article{elbe:05,
  author = {L. Eldén and F. Berntsson},
  title = {A stability estimate for a Cauchy problem for an elliptic partial differential equation},
  journal = {Inverse Problems},
  year = {2005},
  volume = {21},
  pages = {1643-1653}
}
Eldén, L., Hansen, P. and Rojas, M. Computing Functionals Defined on Solutions of Large-Scale Discrete Ill-Posed Problems

[BibTeX]

 2005 BIT
Vol. 45, pp. 329 - 340 		 article  
BibTeX: 
@article{elharo:05,
  author = {L. Eldén and P.C. Hansen and M. Rojas},
  title = {Computing Functionals Defined on Solutions of Large-Scale Discrete Ill-Posed Problems},
  journal = {BIT},
  year = {2005},
  volume = {45},
  pages = {329 - 340}
}
Eldén, L. and Savas, B. The Maximum Likelihood Estimate in Reduced-Rank Regression

[BibTeX]

 2005 Numerical Linear Algebra
Vol. 12, pp. 731-741 		 article  
BibTeX: 
@article{elsa:05,
  author = {L. Eldén and B. Savas},
  title = {The Maximum Likelihood Estimate in Reduced-Rank Regression},
  journal = {Numerical Linear Algebra},
  year = {2005},
  volume = {12},
  pages = {731-741}
}
Park, H. and Eldén, L. Matrix rank reduction for data analysis and feature extraction

[BibTeX]

 2005 Handbook of parallel computing and statistics  incollection  
BibTeX: 
@incollection{pael:05,
  author = {H. Park and L. Eldén},
  title = {Matrix rank reduction for data analysis and feature extraction},
  booktitle = {Handbook of parallel computing and statistics},
  publisher = {CRC Press},
  year = {2005}
}
Eldén, L. Partial Least Squares vs. Lanczos Bidiagonalization I: Analysis of a Projection Method for Multiple Regression

[BibTeX]

 2004 Comput. Statist. Data Anal.
Vol. 46, pp. 11-31 		 article  
BibTeX: 
@article{el02,
  author = {L. Eldén},
  title = {Partial Least Squares vs. Lanczos Bidiagonalization I: Analysis of a Projection Method for Multiple Regression},
  journal = {Comput. Statist. Data Anal.},
  year = {2004},
  volume = {46},
  pages = {11-31}
}
Eldén, L. Solving quadratically constrained least squares problems using a differential-geometric approach

[BibTeX]

 2002 BIT
Vol. 42, pp. 323 - 335 		 article  
BibTeX: 
@article{el01,
  author = {Lars Eldén},
  title = {Solving quadratically constrained least squares problems using a differential-geometric approach },
  journal = {BIT},
  year = {2002},
  volume = {42},
  pages = {323 - 335}
}
Lundström, E. and Eldén, L. Adaptive Eigenvalue Computations using Newton's Method on the Grassmann Manifold

[Abstract] [BibTeX]

 2002 SIAM J. Matrix Anal. Appl.
Vol. 23, pp. 819-839 		 article  
Abstract: We consider the problem of updating an invariant subspace of a large and structured Hermitian matrix when the matrix is modified slightly. The problem can be formulated as that of computing stationary values of a certain function with orthogonality constraints. The constraint is formulated as the requirement that the solution must be on the Grassmann manifold, and Newton?s method on the manifold is used. In each Newton iteration a Sylvester equation is to be solved. We discuss the properties of the Sylvester equation and conclude that for large problems preconditioned iterative methods can be used. Preconditioning techniques are discussed Numerical examples from signal subspace computations are given in which the matrix is Toeplitz and we compute a partial singular value decomposition corresponding to the largest singular values. Further we solve numerically the problem of computing the smallest eigenvalues and corresponding eigenvectors of a large sparse matrix that has been slightly modified.
BibTeX: 
@article{luel:02,
  author = {E.~Lundström and L.~Eldén},
  title = {Adaptive Eigenvalue Computations using Newton's Method on the Grassmann Manifold},
  journal = {SIAM J. Matrix Anal. Appl.},
  year = {2002},
  volume = {23},
  pages = {819-839}
}
Simoncini, V. and Eldén, L. Inexact Rayleigh Quotient-Type Methods for Eigenvalue Computations

[BibTeX]

 2002 BIT
Vol. 42, pp. 159-182 		 article  
BibTeX: 
@article{siel:01,
  author = {V. Simoncini and L. Eldén},
  title = {Inexact Rayleigh Quotient-Type Methods for Eigenvalue Computations},
  journal = {BIT},
  year = {2002},
  volume = {42},
  pages = {159-182}
}
Berntsson, F. and Eldén, L. Numerical Solution of a Cauchy Problem for the Laplace Equation

[BibTeX]

 2001 Inverse Problems
Vol. 17, pp. 839-854 		 article  
BibTeX: 
@article{beel:01,
  author = {F.~Berntsson and Lars Eldén},
  title = {Numerical Solution of a Cauchy Problem for the Laplace Equation},
  journal = {Inverse Problems},
  year = {2001},
  volume = {17},
  pages = {839-854}
}
Kim, M., Park, H. and Eldén, L. Comparison of Algorithms for Toeplitz Least Squares and Symmetric Positive Definite Linear Systems

[BibTeX]

 2001 Contemporary Mathematics
Vol. 281, pp. 73-99 		 article  
BibTeX: 
@article{kipael:01,
  author = {Myungwon Kim and H. Park and L. Eldén },
  title = {Comparison of Algorithms for Toeplitz Least Squares and Symmetric Positive Definite Linear Systems},
  journal = {Contemporary Mathematics},
  year = {2001},
  volume = {281},
  pages = {73-99}
}
Berntsson, F. and Eldén, L. Numerical Solution of an Inverse Steady State Heat Conduction Problem

[BibTeX]

 2000 Inverse Problems in Engineering Mechanics. International Symposium on Inverse Problems in Engineering Mechanics 2000 (ISIP 2000), Nagano, Japan  inproceedings  
BibTeX: 
@inproceedings{beel:00a,
  author = {F.~Berntsson and Lars Eldén},
  title = {Numerical Solution of an Inverse Steady State Heat Conduction Problem},
  booktitle = {Inverse Problems in Engineering Mechanics. International Symposium on Inverse Problems in Engineering Mechanics 2000 (ISIP 2000), Nagano, Japan},
  publisher = {Elsevier},
  year = {2000}
}
Berntsson, F. and Eldén, L. An Inverse Heat Conduction Problem and an Application to Heat Treatment of Aluminium

[BibTeX]

 2000 Inverse Problems in Engineering Mechanics II. International Symposium on Inverse Problems in Engineering Mechanics 2000 (ISIP 2000), Nagano, Japan, pp. 99-106  inproceedings  
BibTeX: 
@inproceedings{beel:00c,
  author = {F.~Berntsson and Lars Eldén},
  title = {An Inverse Heat Conduction Problem and an Application to Heat Treatment of Aluminium},
  booktitle = {Inverse Problems in Engineering Mechanics II. International Symposium on Inverse Problems in Engineering Mechanics 2000 (ISIP 2000), Nagano, Japan},
  publisher = {Elsevier},
  year = {2000},
  pages = {99-106}
}
Eldén, L., Berntsson, F. and Regińska, T. Wavelet and Fourier Methods for Solving the Sideways Heat Equation

[BibTeX]

 2000 SIAM J. Sci. Comput.
Vol. 21(6), pp. 2187-2205 		 article  
BibTeX: 
@article{elber:00,
  author = {L. Eldén and F. Berntsson and T. Regińska},
  title = {Wavelet and Fourier Methods for Solving the Sideways Heat Equation},
  journal = {SIAM J. Sci. Comput.},
  year = {2000},
  volume = {21},
  number = {6},
  pages = {2187--2205}
}
Park, H. and Eldén, L. Schur-type Methods for Solving Least Squares Problems with Toeplitz Structure

[BibTeX]

 2000 SIAM J. Scient. Comput
Vol. 22, pp. 406-430 		 article  
BibTeX: 
@article{pael00,
  author = {H. Park and L. Eldén},
  title = {Schur-type Methods for Solving Least Squares Problems with Toeplitz Structure},
  journal = {SIAM J. Scient. Comput},
  year = {2000},
  volume = {22},
  pages = {406-430}
}
Regińska, T. and Eldén, L. Stability and Convergence of a Wavelet-Galerkin Method for the Sideways Heat Equation

[BibTeX]

 2000 J. Inverse Ill-Posed Problems
Vol. 8, pp. 31-49 		 article  
BibTeX: 
@article{reel:00,
  author = {T. Regińska and L. Eldén},
  title = {Stability and Convergence of a Wavelet-Galerkin Method for the Sideways Heat Equation},
  journal = {J. Inverse Ill-Posed Problems},
  year = {2000},
  volume = {8},
  pages = {31-49}
}
Eldén, L. and Park, H. A Procrustes Problem on the Stiefel Manifold

[BibTeX]

 1999 Numer. Math.
Vol. 82, pp. 599-619 		 article  
BibTeX: 
@article{elpa:99,
  author = {L. Eldén and H. Park},
  title = {A Procrustes Problem on the Stiefel Manifold},
  journal = {Numer. Math.},
  year = {1999},
  volume = {82},
  pages = {599-619}
}
Dax, A. and Eldén, L. Approximating Minimum Norm Solutions of Rank-deficient Least Squares Problems

[BibTeX]

 1998 Numerical Linear Algebra Appl.
Vol. 5, pp. 79-99 		 article  
BibTeX: 
@article{dael:98,
  author = {A. Dax and L. Eldén},
  title = {Approximating Minimum Norm Solutions of Rank-deficient Least Squares Problems},
  journal = {Numerical Linear Algebra Appl.},
  year = {1998},
  volume = {5},
  pages = {79-99}
}
Eldén, L. and Berntsson, F. Spectral and Wavelet Methods for Solving an Inverse Heat Conduction Problem

[BibTeX]

 1998 International Symposium on Inverse Problems in Engineering Mechanics  inproceedings  
BibTeX: 
@inproceedings{elbe:98,
  author = {L. Eldén and F. Berntsson},
  title = {Spectral and Wavelet Methods for Solving an Inverse Heat Conduction Problem},
  booktitle = {International Symposium on Inverse Problems in Engineering Mechanics},
  year = {1998}
}
Berntsson, F., Eldén, L., Garcia-Padron, R. and Loyd, D. A Comparison of Three Numerical Methods for an Inverse Heat Conduction Problem and an Industrial Application

[BibTeX]

 1997 Proceedings of the 10th International Conference on Numerical Methods in Thermal Problems  inproceedings  
BibTeX: 
@inproceedings{begl:97,
  author = {F. Berntsson and L. Eldén and R. Garcia-Padron and D. Loyd},
  title = {A Comparison of Three Numerical Methods for an Inverse Heat Conduction Problem and an Industrial Application},
  booktitle = {Proceedings of the 10th International Conference on Numerical Methods in Thermal Problems},
  year = {1997}
}
Eldén, L. Solving the Sideways Heat Equation by a 'Method of Lines'

[BibTeX]

 1997 J. Heat Transfer, Trans. ASME
Vol. 119, pp. 406-412 		 article  
BibTeX: 
@article{eld:ca:96a,
  author = {L.~Eldén},
  title = {Solving the Sideways Heat Equation by a 'Method of Lines'},
  journal = {J. Heat Transfer, Trans. ASME},
  year = {1997},
  volume = {119},
  pages = {406-412}
}
Lamm, P. and Eldén, L. Numerical Solution of First-Kind Volterra Equations by Sequential Tikhonov Regularization

[BibTeX]

 1997 SIAM J. Numer. Anal.
Vol. 34, pp. 1432-1450 		 article  
BibTeX: 
@article{lael:97,
  author = {P. Lamm and L. Eldén},
  title = {Numerical Solution of First-Kind Volterra Equations by Sequential Tikhonov Regularization},
  journal = {SIAM J. Numer. Anal.},
  year = {1997},
  volume = {34},
  pages = {1432--1450}
}
Park, H. and Eldén, L. Stability Analysis and Fast Algorithms for Triangularization of Toeplitz Matrices

[BibTeX]

 1997 Numer. Math.
Vol. 76, pp. 383-402 		 article  
BibTeX: 
@article{pael:97,
  author = {H. Park and L. Eldén},
  title = {Stability Analysis and Fast Algorithms for Triangularization of Toeplitz Matrices},
  journal = {Numer. Math.},
  year = {1997},
  volume = {76},
  pages = {383-402}
}
Regińska, T. and Eldén, L. Solving the Sideways Heat Equation by a wavelet-Galerkin Method

[BibTeX]

 1997 Inverse Problems
Vol. 13, pp. 1093-1106 		 article  
BibTeX: 
@article{reel:97,
  author = {T. Regińska and L. Eldén},
  title = {Solving the Sideways Heat Equation by a wavelet-Galerkin Method},
  journal = {Inverse Problems},
  year = {1997},
  volume = {13},
  pages = {1093-1106}
}
Eldén, L. and Park, H. Perturbation and Error Analyses for Block Downdating of a Cholesky Decomposition

[BibTeX]

 1996 BIT
Vol. 36, pp. 239-255 		 article  
BibTeX: 
@article{elpa:96,
  author = {L. Eldén and H. Park},
  title = {Perturbation and Error Analyses for Block Downdating of a Cholesky Decomposition},
  journal = {BIT},
  year = {1996},
  volume = {36},
  pages = {239-255}
}
Eldén, L. and Sjöström, E. Fast Computation of the Principal Singular Vectors of Toeplitz Matrices arising in Exponential Data Modelling

[BibTeX]

 1996 Signal Processing
Vol. 50, pp. 151-164 		 article  
BibTeX: 
@article{elsj:96,
  author = {L.~Eldén and E.~Sjöström},
  title = {Fast Computation of the Principal Singular Vectors of Toeplitz Matrices arising in Exponential Data Modelling},
  journal = {Signal Processing},
  year = {1996},
  volume = {50},
  pages = {151--164}
}
Eldén, L. Numerical Solution of the Sideways Heat Equation by Difference Approximation in Time

[BibTeX]

 1995 Inverse Problems
Vol. 11, pp. 913-923 		 article  
BibTeX: 
@article{eldca95a,
  author = {L.~Eldén},
  title = {Numerical Solution of the Sideways Heat Equation by Difference Approximation in Time},
  journal = {Inverse Problems},
  year = {1995},
  volume = {11},
  pages = {913-923}
}
Park, H. and Eldén, L. Downdating the Rank-Revealing URV Decomposition

[BibTeX]

 1995 SIAM J. Matrix Anal. Appl.
Vol. 16, pp. 138-155 		 article  
BibTeX: 
@article{pael95,
  author = {H. Park and L. Eldén},
  title = {Downdating the Rank-Revealing URV Decomposition},
  journal = {SIAM J. Matrix Anal. Appl.},
  year = {1995},
  volume = {16},
  pages = {138-155}
}
Björck, A., Park, H. and Eldén, L. Accurate Downdating of Least Squares Solutions

[BibTeX]

 1994 SIAM J. Matrix Anal. Appl.
Vol. 15, pp. 549-568 		 article  
BibTeX: 
@article{bjpael:94,
  author = {A. Björck and H. Park and L. Eldén},
  title = {Accurate Downdating of Least Squares Solutions},
  journal = {SIAM J. Matrix Anal. Appl.},
  year = {1994},
  volume = {15},
  pages = {549-568}
}
Eldén, L. and Park, H. Block Downdating of Least Squares Solutions

[BibTeX]

 1994 SIAM J. Matrix Anal. Appl.
Vol. 15, pp. 1018-1034 		 article  
BibTeX: 
@article{elpa:94,
  author = {L. Eldén and H. Park},
  title = {Block Downdating of Least Squares Solutions},
  journal = {SIAM J. Matrix Anal. Appl.},
  year = {1994},
  volume = {15},
  pages = {1018-1034}
}
Eldén, L. and Park, H. Perturbation Analysis for Block Downdating of a Cholesky Decomposition

[BibTeX]

 1994 Numerische Mathematik
Vol. 68, pp. 457-467 		 article  
BibTeX: 
@article{elpa:94a,
  author = {L. Eldén and H. Park},
  title = {Perturbation Analysis for Block Downdating of a Cholesky Decomposition},
  journal = {Numerische Mathematik},
  year = {1994},
  volume = {68},
  pages = {457-467}
}
Park, H., Van Huffel, S. and Eldén, L. Fast Algorithms for Exponential Data Modeling

[BibTeX]

 1994
Vol. 4IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 25-28 		 inproceedings  
BibTeX: 
@inproceedings{phe:94,
  author = {H.~Park and S.~Van Huffel and L.~Eldén},
  title = {Fast Algorithms for Exponential Data Modeling},
  booktitle = {IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)},
  publisher = {IEEE, New York},
  year = {1994},
  volume = {4},
  pages = {25-28}
}
Park, H. and Eldén, L. Fast and Accurate Toeplitz Matrix Triangularization for Linear Prediction

[BibTeX]

 1993 VLSI Signal Processing VI  inproceedings  
BibTeX: 
@inproceedings{pael:93c,
  author = {H. Park and L. Eldén},
  title = {Fast and Accurate Toeplitz Matrix Triangularization for Linear Prediction},
  booktitle = {VLSI Signal Processing VI},
  year = {1993}
}
Eldén, L. Algorithms for the computation of functionals defined on the solution of a discrete ill-posed problem

[BibTeX]

 1990 BIT
Vol. 30, pp. 466-483 		 article  
BibTeX: 
@article{eld:il:90,
  author = {L.~Eldén},
  title = {Algorithms for the computation of functionals defined on the solution of a discrete ill-posed problem},
  journal = {BIT},
  year = {1990},
  volume = {30},
  pages = {466-483}
}
Seidman, T. and L.Eldén An Optimal Filtering Method for the Sideways Heat Equation

[BibTeX]

 1990 Inverse Probl.
Vol. 6, pp. 681-696 		 article  
BibTeX: 
@article{seield90,
  author = {T. Seidman and L.Eldén},
  title = {An Optimal Filtering Method for the Sideways Heat Equation},
  journal = {Inverse Probl.},
  year = {1990},
  volume = {6},
  pages = {681-696}
}
Eldén, L. Hyperbolic Approximations for a Cauchy Problem for the Heat Equation

[BibTeX]

 1988 Inverse Problems
Vol. 4, pp. 59-70 		 article  
BibTeX: 
@article{eld:88,
  author = {L.~Eldén},
  title = {Hyperbolic Approximations for a Cauchy Problem for the Heat Equation},
  journal = {Inverse Problems},
  year = {1988},
  volume = {4},
  pages = {59-70}
}
Eldén, L. Approximations for a Cauchy Problem for the Heat Equation

[BibTeX]

 1987 Inverse Problems
Vol. 3, pp. 263-273 		 article  
BibTeX: 
@article{eld87,
  author = {L.~Eldén},
  title = {Approximations for a Cauchy Problem for the Heat Equation},
  journal = {Inverse Problems},
  year = {1987},
  volume = {3},
  pages = {263-273}
}
Eldén, L. and Schreiber, R. An application of systolic arrays to linear, discrete ill-posed problems

[BibTeX]

 1986 SIAM J. Sci. Stat. Comp.
Vol. 7, pp. 892-903 		 article  
BibTeX: 
@article{elsc:86,
  author = {L. Eldén and R. Schreiber},
  title = {An application of systolic arrays to linear, discrete ill-posed problems},
  journal = {SIAM J. Sci. Stat. Comp.},
  year = {1986},
  volume = {7},
  pages = {892-903}
}
Eldén, L. and Schreiber, R. A systolic array for the regularization of ill-conditioned least squares problems with triangular Toeplitz matrix

[BibTeX]

 1986 Lin. Alg. Appl.
Vol. 77, pp. 137-147 		 article  
BibTeX: 
@article{elsc:86a,
  author = {L. Eldén and R. Schreiber},
  title = {A systolic array for the regularization of ill-conditioned least squares problems with triangular Toeplitz matrix},
  journal = {Lin. Alg. Appl.},
  year = {1986},
  volume = {77},
  pages = {137-147}
}
Eldén, L. An Efficient Algorithm for the Regularization of Ill-Conditioned Least Squares Problems with Triangular Toeplitz Matrix

[BibTeX]

 1984 SIAM J. Sci. Stat. Comput.
Vol. 5, pp. 229-236 		 article  
BibTeX: 
@article{eld:84a,
  author = {L.~Eldén},
  title = {An Efficient Algorithm for the Regularization of Ill-Conditioned Least Squares Problems with Triangular Toeplitz Matrix},
  journal = {SIAM J. Sci. Stat. Comput.},
  year = {1984},
  volume = {5},
  pages = {229-236}
}
Eldén, L. An Algorithm for the Regularization of Ill-Conditioned, Banded Least Squares Problems

[BibTeX]

 1984 SIAM J. Sci. Stat. Comput.
Vol. 5, pp. 237-254 		 article  
BibTeX: 
@article{eld:84i,
  author = {L.~Eldén},
  title = {An Algorithm for the Regularization of Ill-Conditioned, Banded Least Squares Problems},
  journal = {SIAM J. Sci. Stat. Comput.},
  year = {1984},
  volume = {5},
  pages = {237-254}
}
Eldén, L. A Note on the Computation of the Generalized Cross-Validation Function for Ill-Conditioned Least Squares Problems

[BibTeX]

 1984 BIT
Vol. 24, pp. 467-472 		 article  
BibTeX: 
@article{eld84b,
  author = {L.~Eldén},
  title = {A Note on the Computation of the Generalized Cross-Validation Function for Ill-Conditioned Least Squares Problems},
  journal = {BIT},
  year = {1984},
  volume = {24},
  pages = {467-472}
}
Eldén, L. A Weighted Pseudoinverse, Generalized Singular Values, and Constrained Least Squares Problems

[BibTeX]

 1982 BIT
Vol. 22, pp. 487-502 		 article  
BibTeX: 
@article{eld82,
  author = {L.~Eldén},
  title = {A Weighted Pseudoinverse, Generalized Singular Values, and Constrained Least Squares Problems},
  journal = {BIT},
  year = {1982},
  volume = {22},
  pages = {487-502}
}
Eldén, L. Time discretization of the backward solution of parabolic equations, Part I

[BibTeX]

 1982 Math. Comp.
Vol. 39, pp. 53-68 		 article  
BibTeX: 
@article{eld82a,
  author = {L. Eldén},
  title = {Time discretization of the backward solution of parabolic equations, Part I},
  journal = {Math. Comp.},
  year = {1982},
  volume = {39},
  pages = {53-68}
}
Eldén, L. Time discretization of the backward solution of parabolic equations, Part II

[BibTeX]

 1982 Math. Comp.
Vol. 39, pp. 69-84 		 article  
BibTeX: 
@article{eld82b,
  author = {L. Eldén},
  title = {Time discretization of the backward solution of parabolic equations, Part II},
  journal = {Math. Comp.},
  year = {1982},
  volume = {39},
  pages = {69-84}
}
Eldén, L. Perturbation theory for the least squares problem with linear equality constraints

[BibTeX]

 1980 SIAM J. Numer. Anal.
Vol. 17, pp. 338-350 		 article  
BibTeX: 
@article{eld80,
  author = {L. Eldén},
  title = {Perturbation theory for the least squares problem with linear equality constraints},
  journal = {SIAM J. Numer. Anal.},
  year = {1980},
  volume = {17},
  pages = {338-350}
}
Eldén, L. Algorithms for the Regularization of Ill-conditioned Least Squares Problems

[BibTeX]

 1977 BIT
Vol. 17, pp. 134-145 		 article  
BibTeX: 
@article{eld:77,
  author = {L.~Eldén},
  title = {Algorithms for the Regularization of Ill-conditioned Least Squares Problems},
  journal = {BIT},
  year = {1977},
  volume = {17},
  pages = {134-145}
}
Eldén, L. Stepwise regression analysis with orthogonal transformations

[BibTeX]

 1972 (LiTH-MAT-R-1972-2)  techreport  
BibTeX: 
@techreport{eld72,
  author = {L. Eldén},
  title = {Stepwise regression analysis with orthogonal transformations},
  year = {1972},
  number = {LiTH-MAT-R-1972-2}
}