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The Lanczos and Conjugate Gradient Algorithms

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The Lanczos and Conjugate Gradient Algorithms

From Theory to Finite Precision Computations

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The Lanczos and Conjugate Gradient Algorithms by Gerard Meurant
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Description

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 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.

Author Biography

Gerard Meurant is Director of Research in the military applications division at Commissariat ... l'Energie Atomique (CEA) in Bruyeres le Chatel, France. He is the author of Computer Solution of Large Linear Systems (North-Holland, 1999) and serves on the editorial boards of the International Journal of High Speed Computing and Numerical Algorithms. In 1988 Meurant was awarded the Prix CEA and in 1995 the Palmes Academiques, an honor presented each year by the French Ministry of Education.
Release date NZ
August 1st, 2006
Country of Publication
United States
Imprint
Society for Industrial & Applied Mathematics,U.S.
Pages
184
Dimensions
170x247x19
ISBN-13
9780898716160
Product ID
1836147

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