• Publications
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A weighted pseudoinverse, generalized singular values, and constrained least squares problems
The weighted pseudoinverse providing the minimum semi-norm solution of the weighted linear least squares problem is studied. It is shown that it has properties analogous to those of the Moore-PenroseExpand
  • 153
  • 21
Algorithms for the regularization of ill-conditioned least squares problems
Two regularization methods for ill-conditioned least squares problems are studied from the point of view of numerical efficiency. The regularization methods are formulated as quadraticallyExpand
  • 273
  • 18
Matrix methods in data mining and pattern recognition
  • L. Eldén
  • Computer Science, Mathematics
  • Fundamentals of algorithms
  • 1 April 2007
TLDR
Preface Part I. Linear Algebra Concepts and Matrix Decompositions: 1. Expand
  • 189
  • 14
Inexact Rayleigh Quotient-Type Methods for Eigenvalue Computations
AbstractWe consider the computation of an eigenvalue and corresponding eigenvector of a Hermitian positive definite matrix A ∈ $$\mathbb{C}^{n \times n}$$ , assuming that good approximations of theExpand
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Handwritten digit classification using higher order singular value decomposition
TLDR
In this paper we present two algorithms for handwritten digit classification based on the higher order singular value decomposition (HOSVD) of a tensor. Expand
  • 197
  • 11
A Newton-Grassmann Method for Computing the Best Multilinear Rank-(r1, r2, r3) Approximation of a Tensor
TLDR
We derive a Newton method for computing the best rank-$(r_1,r_2, r_3) approximation of a given tensor $\mathcal{A}$ on a product of Grassmann manifolds. Expand
  • 127
  • 8
  • PDF
Numerical linear algebra in data mining
  • L. Eldén
  • Computer Science
  • Acta Numerica
  • 1 May 2006
TLDR
We give an overview of linear algebra methods in text mining (information retrieval), pattern recognition (classification of handwritten digits), and PageRank computations. Expand
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  • 7
  • PDF
Numerical solution of the sideways heat equation by difference approximation in time
We consider a Cauchy problem for the heat equation in the quarter plane, where data are given at x=1 and a solution is sought in the interval 0<x<1. This sideways heat equation is a model of aExpand
  • 106
  • 7
Partial least-squares vs. Lanczos bidiagonalization - I: analysis of a projection method for multiple regression
  • L. Eldén
  • Mathematics, Computer Science
  • Comput. Stat. Data Anal.
  • 28 May 2004
TLDR
An analysis of the partial least-squares method (PLS) for computing a projection onto a lower-dimensional subspace. Expand
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  • 6
  • PDF
Numerical solution of a Cauchy problem for the Laplace equation
We consider a two-dimensional steady state heat conduction problem. The Laplace equation is valid in a domain with a hole. Temperature and heat-flux data are specified on the outer boundary, and weExpand
  • 107
  • 6
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