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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations

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

Meurant, Gérard

Paperback

Series: Software, Environments and Tools, Book 19

General Mathematics

Currently unavailable to order

ISBN10: 0898716160
ISBN13: 9780898716160
Publisher: Society for Industrial and Applied Mathematic
Published: Aug 1 2006
Pages: 184
Language: English
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.

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