The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations (Software, Environments and Tools): 19 (Software, Environments and Tools, Series Number 19) - Softcover

Meurant, Gérard

Softcover

ISBN 10: 0898716160 ISBN 13: 9780898716160

Publisher: Society for Industrial and Applied Mathematics, 2006

Synopsis

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.

About this title

About the Author

Gérard Meurant is Director of Research in the military applications division at Commissariat à l'Énergie Atomique (CEA) in Bruyères le Châtel, 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 Académiques, an honor presented each year by the French Ministry of Education.

From the Inside Flap

"No present book comes near this one in the range and depth of treatment of these two extremely important methods the Lanczos algorithm and the method of conjugate gradients." Chris Paige, School of Computer Science, McGill University.

Edition details

• Publisher: Society for Industrial and Applied Mathematics
• Publication date: 2006
• Language: English
• ISBN 10: 0898716160
• ISBN 13: 9780898716160
• Binding: Paperback
• Number of pages: 184