The Lanczos and Conjugate Gradient Algorithms
From Theory to Finite Precision Computations
By (author) Gerard Meurant
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Lanczos and Conjugate Gradient Algorithms by Gerard Meurant
Book DescriptionThis 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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Book DetailsISBN: 9780898716160
(247mm x 170mm x 19mm)
Imprint: Society for Industrial & Applied Mathematics,U.S.
Publisher: Society for Industrial & Applied Mathematics,U.S.
Publish Date: 1-Aug-2006
Country of Publication: United States
Books By Author Gerard Meurant
Matrices, Moments, and Quadrature with Applications, Hardback (November 2009)
Describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. This book provides the mathematical background and explains the theory.
Infinite Dimensional Linear Control Systems, Hardback (July 2005)
Aims to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y(t) = Ay(t) + u(t) that ends at the very frontier of research. This work includes applications to optimal diffusion processes; applications to optimal heat propagation processes; and more.
Troubleshooting Centrifugal Pumps & Their Systems, Hardback (December 2003)
Written for novices, this volume explains how centrifugal pumps and their attendant pipework function, before moving on to the more difficult task of solving problems and troubleshooting such systems.
Agenda Relevance, Hardback (May 2003)» View all books by Gerard Meurant
Identifies practical reasoning as reasoning performed with comparatively few cognitive assets, including resources such as information, time and computational capacity. This work is intended for researchers in logic, belief dynamics, computer science, AI, psychology and neuroscience, linguistics, argumentation theory, and other fields.
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Author Biography - Gerard Meurant
Gerard Meurant is Director of Research in the military applications division at Commissariat ... l'Energie Atomique (CEA) in Bruyeres le Chatel, 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 Academiques, an honor presented each year by the French Ministry of Education.
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