Conjugate Gradient Type Methods for Ill-Posed Problems

Martin Hanke, L E Payne

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English

CRC Press
26 April 1995

Differential calculus & equations

Series: Chapman & Hall/CRC Research Notes in Mathematics Series

The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.

This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more

This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations.

The main tool for the analysis is the connection of conjugate gradient

type methods to real orthogonal polynomials, and elementary

properties of these polynomials. These prerequisites are provided in

a first chapter. Applications to image reconstruction and inverse

heat transfer problems are pointed out, and exemplarily numerical

results are shown for these applications.

By: Martin Hanke
Series edited by: L E Payne
Imprint: CRC Press
Country of Publication: United Kingdom
Volume: 327
Dimensions: Height: 246mm, Width: 174mm, Spine: 279mm
Weight: 258g
ISBN: 9780582273702
ISBN 10: 0582273706
Series: Chapman & Hall/CRC Research Notes in Mathematics Series
Pages: 144
Publication Date: 26 April 1995
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Hanke\, Martin