Oblique projections and standard-form transformations for discrete inverse problems

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Abstract

This tutorial paper considers a specific computational tool for the numerical solution of discrete inverse problems, known as the standard-form transformation, by which we can treat general Tikhonov regularization problems efficiently. In the tradition of B. N. Datta's expositions of numerical linear algebra, we use the close relationship between oblique projections, pseudoinverses, and matrix computations to derive a simple geometric motivation and algebraic formulation of the standard-form transformation.
Original languageEnglish
JournalNumerical Linear Algebra with Applications
Volume20
Issue number2
Pages (from-to)250–258
ISSN1070-5325
DOIs
Publication statusPublished - 2013

Keywords

  • Weighted pseudoinverse
  • Discrete inverse problem
  • Oblique projection

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