The Lanczos And Conjugate Gradient Algorithms

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  • Format: Paperback
  • Copyright: 2006-08-30
  • Publisher: Society for Industrial & Applied
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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

GTrard Meurant is Director of Researcháin the military applications division atáCommissariatáa l'+nergieáAtomiqueá(CEA) ináBruyFres le ChGtel, France. He is the author of Computer Solution of Large Linear Systems (NorthûHolland, 1999) and servesáon the editorial boards of the International Journal of High Speed Computing and Numerical Algorithms.áIná1988 Meurant was awarded the Prix CEA and in 1995 the Palmes AcadTmiques, an honor presented each year by the French Ministry of Education.

Table of Contents

The Lanczos algorithm in exact arithmetic
The CG algorithm in exact arithmetic
A historical perspective on the Lanczos algorithm in finite precision
The Lanczos algorithm in finite precision
The CG algorithm in finite precision
The maximum attainable accuracy
Estimates of norms of the error in finite precision
The preconditioned CG algorithm
Table of Contents provided by Publisher. All Rights Reserved.

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