The Lanczos and conjugate gradient algorithms [electronic resource] : from theory to finite precision computations / Gérard Meurant.
- Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2006.
- Software, environments, tools ; 19.
Software, environments, tools
Software, environments, tools ; SE19
1 online resource (xv, 365 p. ) ill. ;
- Conjugate gradient methods.
Algorithms -- Methodology.
- System Details:
- Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
- The Lanczos and conjugate gradient (CG) algorithms are fascinating numerical algorithms. This book presents the most comprehensive discussion to date of the use of these 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 emphasizes how both algorithms can be used efficiently in finite precision arithmetic, regardless of the growth of rounding errors that occurs. He details the mathematical properties of both algorithms and demonstrates how the CG algorithm is derived from the Lanczos algorithm. 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.
Chapter 1. The Lanczos algorithm in exact arithmetic
Chapter 2. The CG algorithm in exact arithmetic
Chapter 3. A historical perspective on the Lanczos algorithm in finite precision
Chapter 4. The Lanczos algorithm in finite precision
Chapter 5. The CG algorithm in finite precision
Chapter 6. The maximum attainable accuracy
Chapter 7. Estimates of norms of the error in finite precision
Chapter 8. The preconditioned CG algorithm
Chapter 9. Miscellaneous - Appendix.
- Bibliographic Level Mode of Issuance: Monograph
Includes bibliographical references.
Description based on title page of print version.
- Society for Industrial and Applied Mathematics.
- Publisher Number:
- SE19 siam
- Access Restriction:
- Restricted to subscribers or individual electronic text purchasers.
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