By Gérard Meurant

"No current ebook comes close to this one within the variety and intensity of remedy of those vitally important methods—the Lanczos set of rules and the tactic of conjugate gradients." Chris Paige, university of laptop technology, McGill college.   The Lanczos and conjugate gradient (CG) algorithms are attention-grabbing numerical algorithms. This booklet provides the main accomplished dialogue thus far of using those equipment for computing eigenvalues and fixing linear platforms in either specific and floating element mathematics. the writer synthesizes the learn performed during the last 30 years, describing and explaining the "average" habit of those equipment and delivering new perception into their properties in finite precision. Many examples are provided that exhibit major effects got via researchers within the box. the writer emphasizes how either algorithms can be utilized successfully in finite precision mathematics, whatever the progress of rounding blunders that happens. He info the mathematical houses of either algorithms and demonstrates how the CG set of rules is derived from the Lanczos set of rules. lack of orthogonality concerned with utilizing the Lanczos set of rules, how you can enhance the utmost possible accuracy of CG computations, and what changes have to be made while the CG procedure is used with a preconditioner are addressed. This ebook is meant for utilized mathematicians, computational scientists, engineers, and physicists who've an curiosity in linear algebra, numerical research, and partial differential equations. will probably be of curiosity to engineers and scientists utilizing the Lanczos set of rules to compute eigenvalues and the CG set of rules to resolve linear platforms, and to researchers in Krylov subspace tools for symmetric matrices, specifically these thinking about floating element errors research. additionally, it may be utilized in complicated classes on iterative tools or as a accomplished presentation of a well known numerical procedure in ﬁnite precision mathematics. Contents Preface; bankruptcy 1: The Lanczos set of rules in specific mathematics; bankruptcy 2: The CG set of rules in detailed mathematics; bankruptcy three: A old point of view at the Lanczos set of rules in finite precision; bankruptcy four: The Lanczos set of rules in finite precision; bankruptcy five: The CG set of rules in finite precision; bankruptcy 6: the utmost possible accuracy; bankruptcy 7: Estimates of norms of the mistake in finite precision; bankruptcy eight: The preconditioned CG set of rules; bankruptcy nine: Miscellaneous; Appendix; Bibliography; Index.

Read or Download The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations (Software, Environments and Tools) PDF

Best Computational Mathematicsematics books

23 Problems in Systems Neuroscience (Computational Neuroscience Series)

The complexity of the mind and the protean nature of habit stay the main elusive zone of technological know-how, but in addition crucial. van Hemmen and Sejnowski invited 23 specialists from the numerous areas--from evolution to qualia--of structures neuroscience to formulate one challenge each one. even if each one bankruptcy was once written independently and will be learn individually, jointly they supply an invaluable roadmap to the sphere of structures neuroscience and should function a resource of inspirations for destiny explorers of the mind.

Milestones in Matrix Computation: The selected works of Gene H. Golub with commentaries (Oxford Science Publications)

The textual content offers and discusses essentially the most influential papers in Matrix Computation authored through Gene H. Golub, one of many founding fathers of the sphere. the gathering of 21 papers in divided into 5 major components: iterative tools for linear structures, answer of least squares difficulties, matrix factorizations and purposes, orthogonal polynomials and quadrature, and eigenvalue difficulties an commentaries for every quarter are supplied by means of major specialists: Anne Greenbaum, Ake Bjorkc, Nicholas Higham, Walter Gautschi, and G.

Additional resources for The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations (Software, Environments and Tools)

Show sample text content

Rated 4.53 of 5 – based on 9 votes