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The Lanczos and Conjugate Gradient Algorithms

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

£89.00

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  • Author: Gérard Meurant, Commissariat à l'Énergie Atomique, Bruyères le Châtel
  • Date Published: August 2006
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898716160

£ 89.00
Paperback

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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.

    • No present book comes near this one in the range and depth of treatment of these two extremely important methods
    • The author synthesizes the research done over the past 30 years
    • Includes many examples
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    Reviews & endorsements

    '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

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    Product details

    • Date Published: August 2006
    • format: Paperback
    • isbn: 9780898716160
    • length: 184 pages
    • dimensions: 255 x 177 x 19 mm
    • weight: 0.649kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface
    1. The Lanczos algorithm in exact arithmetic
    2. The CG algorithm in exact arithmetic
    3. A historical perspective on the Lanczos algorithm in finite precision
    4. The Lanczos algorithm in finite precision
    5. The CG algorithm in finite precision
    6. The maximum attainable accuracy
    7. Estimates of norms of the error in finite precision
    8. The preconditioned CG algorithm
    9. Miscellaneous
    Appendix
    Bibliography
    Index.

  • Author

    Gérard Meurant, Commissariat à l'Énergie Atomique, Bruyères le Châtel
    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.

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