Lars Eldén

Professor emeritus of Scientific Computing
orcid.org/0000-0003-2281-856X

Matrix Methods in Data Mining and Pattern Recognition

The second edition is available from SIAM.
Review

Recent papers

• Multiway Spectral Graph Partitioning: Cut Functions, Cheeger Inequalities, and a Simple Algorithm. SIAM J. Matrix Anal. Appl. or for download.
• A Krylov-Schur Like Method for Computing the Best Rank-($r_1,r_2,r_3$) Approximation of Large and Sparse Tensors. Numerical Algorithms (open access) Codes
• Spectral Partitioning of Large and Sparse Tensors using Low-Rank Tensor Approximation, Numerical Linear Algebra Appl. (open access)
• Analyzing Large and Sparse Tensor Data using Spectral Low-Rank Approximation, arXiv:2012.07754. PDF
• Solving bilinear tensor least squares problems and application to Hammerstein identification,
  Numer. Lin. Alg. Appl. 2019   PDF  BIBTEX 
• Semi-sparse PCA, Psychometrika 2018  
  PDF   BIBTEX  
• Solving an Ill-Posed Cauchy Problem for a Two-Dimensional Parabolic PDE with Variable Coefficients using a Preconditioned GMRES Method, SISC 2014  
  PDF   BIBTEX  
• Computing Frechet Derivatives in Partial Least Squares Regresssion, LAA 2015  
  PDF   BIBTEX  
• Computing Semantic Clusters by Semantic Mirroring and Spectral Graph Partitioning, Mathematics in Computer Science 2013  
  PDF   BIBTEX   Springer Link
• Solving Ill-Posed Linear Systems with GMRES and a Singular Preconditioner, SIMAX 2012  
  PDF   BIBTEX  
• Perturbation Theory and Optimality Conditions for the Best Multilinear Rank Approximation of a Tensor, SIMAX 2011,   PDF,    BIBTEX
• Krylov-type methods for tensor computations I,  LAA 2012 
   BIBTEX

Introduction to Numerical Computation

The book by Eldén, Wittmeyer-Koch, and Bruun-Nielsen from 2004 is out of print but is now available here for free. PDF

Editor-in-chief of BIT Numerical Mathematics 2015-2018

BIT at Springer

 

Data Analysis

"The traditional rationale within applied mathematics has been to solve or provide insight for equations which describe some part of the physical world. .... But there is a paradigm shift afoot. Mathematics is used to describe data, without the benefit of an interpolating equation or physical principle."
(J. Glimm, Bulletin of the American Mathematical Society, 47, Jan 2010, p. 127-136.)

"The analysis of large data sets to provide understanding, and ultimately knowledge, is one of the fundamental intellectual challenges of our time. It falls to practitioners of the mathematical sciences (mathematics, statistics, and computer science) to devise new methods for carrying out analysis tasks, as well as to construct new models or paradigms for thinking about data."
(Gunnar Carlsson and Robert Ghrist, SIAM News, April 2012).