Matrices That Generate the Same Krylov Residual Spaces Classic Reprint

Anne Greenbaum

ISBN 10: 1334017824 ISBN 13: 9781334017827
Editorial: Forgotten Books, 2019
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New Book. Shipped from UK. Established seller since 2000. N° de ref. del artículo LX-9781334017827

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Excerpt from Matrices That Generate the Same Krylov Residual Spaces

If the matrix A is normal, then h'(z) is one, and it was recently shown in several different ways that this bound is sharp; i.e., that for each Is, there is an initial vector (depending on k) for which equality holds in In many cases of interest. However. The matrix A is not normal and the factor in (7) may be quite large. (see. For instance. [13] for some interesting physical examples.) In such cases. The bound (7) may be a large overestimate of the actual residual.

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Reseña del editor: Excerpt from Matrices That Generate the Same Krylov Residual Spaces

If the matrix A is normal, then h'(z) is one, and it was recently shown in several different ways that this bound is sharp; i.e., that for each Is, there is an initial vector (depending on k) for which equality holds in In many cases of interest. However. The matrix A is not normal and the factor in (7) may be quite large. (see. For instance. [13] for some interesting physical examples.) In such cases. The bound (7) may be a large overestimate of the actual residual.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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Título: Matrices That Generate the Same Krylov ...
Editorial: Forgotten Books
Año de publicación: 2019
Encuadernación: PAP
Condición: New

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Paperback. Condición: New. Print on Demand. Uncover the fascinating connection between non-normal matrices and their eigenvalue distribution in this insightful book. The author meticulously analyzes the convergence behavior of the GMRES method applied to non-normal matrices. Through novel techniques and rigorous analysis, the book establishes equivalencies between the original matrix and various structured matrices, such as unitary and Hermitian matrices. By exploring the behavior of GMRES in these equivalent scenarios, the book sheds light on the role of eigenvalues and pseudo-eigenvalues in determining the convergence rate. This profound investigation not only expands our understanding of matrix analysis but also provides valuable insights into the efficiency of iterative methods for solving linear systems. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781334017827_0

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Anne Greenbaum
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ISBN 10: 1334017824 ISBN 13: 9781334017827
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