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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
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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
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Matrix methods in data mining and pattern recognition
  • L. Eldén
  • Computer Science, Mathematics
  • Fundamentals of algorithms
  • 1 April 2007
Preface Part I. Linear Algebra Concepts and Matrix Decompositions: 1. Expand
  • 189
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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
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
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A Newton-Grassmann Method for Computing the Best Multilinear Rank-(r1, r2, r3) Approximation of a Tensor
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
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  • PDF
Numerical linear algebra in data mining
  • L. Eldén
  • Computer Science
  • Acta Numerica
  • 1 May 2006
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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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
An analysis of the partial least-squares method (PLS) for computing a projection onto a lower-dimensional subspace. Expand
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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
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