Home » The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations by Gérard Meurant
The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations Gérard Meurant

The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations

Gérard Meurant

Published January 1st 2006
ISBN : 9780898716160
Paperback
365 pages
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 About the Book 

This book presents the most comprehensive discussion to date of the use of the Lanczos and CG methods for computing eigenvalues and solving linear systems in both exact and floating point arithmetic. The author synthesizes the research done over theMoreThis book presents the most comprehensive discussion to date of the use of the Lanczos and CG methods for computing eigenvalues and solving linear systems in both exact and floating point arithmetic. The author synthesizes the research done over the past 30 years, describing and explaining the average behavior of these methods and providing new insight into their properties in finite precision. Many examples are given that show significant results obtained by researchers in the field. The author details the mathematical properties of both algorithms and emphasizes how they can be used efficiently in finite precision arithmetic, regardless of the growth of rounding errors that occurs. Loss of orthogonality involved with using the Lanczos algorithm, ways to improve the maximum attainable accuracy of CG computations, and what modifications need to be made when the CG method is used with a preconditioner are addressed.