Oblique projections and standard‐form transformations for discrete inverse problems. Issue 2 (18th October 2011)

• Record Type: Journal Article
• Authors: Hansen, Per Christian
• Other Names: Chu Eric guestEditor.; Lin Wen‐wei guestEditor.; Reichel Lothar guestEditor.
• Is Part Of: Numerical linear algebra with applications. Volume 20:Issue 2(2013:Mar.)
• Page Start: 250
• Page End: 258
• Publication Date: 2011-10-18
• Subjects: oblique projection -- weighted pseudoinverse -- discrete inverse problem; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.802
• Languages: English
• ISSNs: 1070-5325

Abstract

SUMMARY: 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. Copyright © 2011 John Wiley & Sons, Ltd.