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Conjugate Gradient Type Methods for Ill-Posed Problems
Af: Martin Hanke Engelsk Paperback
SPAR
kr 90
Conjugate Gradient Type Methods for Ill-Posed Problems
Af: Martin Hanke Engelsk Paperback
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 Most of the results are as yet unpublished, or obscured in the Russian literature.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 Most of the results are as yet unpublished, or obscured in the Russian literature.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.
Produktdetaljer
Sprog: Engelsk
Sider: 142
ISBN-13: 9780367449117
Indbinding: Paperback
Udgave:
ISBN-10: 0367449110
Udg. Dato: 2 dec 2019
Længde: 13mm
Bredde: 176mm
Højde: 245mm
Oplagsdato: 2 dec 2019
Forfatter(e): Martin Hanke
Forfatter(e) Martin Hanke


Kategori Differentialregning & ligninger


Sprog Engelsk


Indbinding Paperback


Sider 142


Udgave


Længde 13mm


Bredde 176mm


Højde 245mm


Udg. Dato 2 dec 2019


Oplagsdato 2 dec 2019

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