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  2. Regning og matematisk analyse
  3. Differentialregning & ligninger

Conjugate Gradient Type Methods for Ill-Posed Problems

Af: Martin Hanke Engelsk Paperback

Conjugate Gradient Type Methods for Ill-Posed Problems

Af: Martin Hanke Engelsk Paperback
Tjek vores konkurrenters priser
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 Most of the results are as yet unpublished, or obscured in the Russian literature.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.
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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.
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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 142
ISBN-13: 9780367449117
Indbinding: Paperback
Udgave:
ISBN-10: 0367449110
Kategori: Differentialregning & ligninger
Udg. Dato: 2 dec 2019
Længde: 13mm
Bredde: 245mm
Højde: 176mm
Forlag: Taylor & Francis Ltd
Oplagsdato: 2 dec 2019
Forfatter(e): Martin Hanke
Forfatter(e) Martin Hanke

Kategori Differentialregning & ligninger

ISBN-13 9780367449117

Sprog Engelsk

Indbinding Paperback

Sider 142

Udgave

Længde 13mm

Bredde 245mm

Højde 176mm

Udg. Dato 2 dec 2019

Oplagsdato 2 dec 2019

Forlag Taylor & Francis Ltd

Kategori sammenhænge