0845 474 4572
info@eurospanbookstore.com

Special order: Usually despatched within 10-14 days

The Lanczos and Conjugate Gradient Algorithms

From Theory to Finite Precision Computations

Gerard Meurant (author)

ISBN: 9780898716160

Publication Date: Aug 2006

Format: Paperback

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.
£120.00

Special order: will dispatch within 5 days

  • Full Description
  • More Information
  • Table of Contents
  • Customer Reviews
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" behaviour 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.
Pages 380
Dimensions 229 x 152
Date Published 30 Aug 2006
Publisher SIAM - Society for Industrial and Applied Mathematics
Series Software Environments and Tools
Series Part 19
Subject/s Applied mathematics   Computer science   Maths for engineers  
  • Preface
  • 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
  • Bibliography
  • Index.

Write Your Own Review

Only registered users can write reviews. Please, log in or register

Post your comment

Eurospan Bookstore