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Paperback. Condición: New. This first title in SIAM's Spotlights book series is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem.The book's central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together.This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.…

Paperback. Condición: New. Print on Demand. Uncover the fascinating connection between non-normal matrices and their eigenvalue distribution in this insightful book. The author meticulously analyzes the convergence behavior of the GMRES method applied to non-normal matrices. Through novel techniques and rigorous analysis, the book establishes equivalencies between the original matrix and various structured matrices, such as unitary and Hermitian matrices. By exploring the behavior of GMRES in these equivalent scenarios, the book sheds light on the role of eigenvalues and pseudo-eigenvalues in determining the convergence rate. This profound investigation not only expands our understanding of matrix analysis but also provides valuable insights into the efficiency of iterative methods for solving linear systems. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item.…

Condición: New. A book linking matrix computation with analytic techniques to explore the links between different stages of solving an applied problem. Num Pages: 114 pages. BIC Classification: PBK. Category: (U) Tertiary Education (US: College). Dimension: 181 x 254 x 13. Weight in Grams: 220. . 2014. Paperback. . . . . …

Condición: New. pp. 114.

Condición: New.

Condición: New. pp. 114.

Condición: As New. Unread book in perfect condition.

Condición: New. A book linking matrix computation with analytic techniques to explore the links between different stages of solving an applied problem. Num Pages: 114 pages. BIC Classification: PBK. Category: (U) Tertiary Education (US: College). Dimension: 181 x 254 x 13. Weight in Grams: 220. . 2014. Paperback. . . . . Books ship from the US and Ireland. …

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Buch. Condición: Neu. Neuware - This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.…

Paperback. Condición: new. Paperback. The mathematical theory of Krylov subspace methods with a focus on solving systems of linear algebraic equations is given a detailed treatment in this principles-based book. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments, and therefore Krylov subspace methods can be viewed asmatching moments model Describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods, challenging some common assumptions and justifications of standard approaches. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

Paperback. Condición: New. This first title in SIAM's Spotlights book series is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem.The book's central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together.This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.…

Condición: New. Describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods, challenging some common assumptions and justifications of standard approaches. Series: Numerical Mathematics & Scientific Computation. Num Pages: 408 pages, 43 b/w line drawings. BIC Classification: PBF; PBWH; PDE; TGB. Category: (UP) Postgraduate, Research & Scholarly. Dimension: 236 x 154 x 26. Weight in Grams: 600. . 2015. 1st Edition. Paperback. . . . .…

Paperback. Condición: Brand New. 1st edition. 408 pages. 9.13x5.98x0.94 inches. In Stock.

Condición: New. Describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods, challenging some common assumptions and justifications of standard approaches. Series: Numerical Mathematics & Scientific Computation. Num Pages: 408 pages, 43 b/w line drawings. BIC Classification: PBF; PBWH; PDE; TGB. Category: (UP) Postgraduate, Research & Scholarly. Dimension: 236 x 154 x 26. Weight in Grams: 600. . 2015. 1st Edition. Paperback. . . . . Books ship from the US and Ireland.…

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Hardcover. Condición: Like New. LIKE NEW. SHIPS FROM MULTIPLE LOCATIONS. book.

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Condición: New. Print on Demand pp. 36.

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Hardcover. Condición: new. Hardcover. The mathematical theory of Krylov subspace methods with a focus on solving systems of linear algebraic equations is given a detailed treatment in this principles-based book. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments, and therefore Krylov subspace methods can be viewed asmatching moments model reduction. This allows enlightening reformulations of questions from matrix computations into the language of orthogonal polynomials, Gauss-Christoffel quadrature, continuedfractions, and, more generally, of Vorobyev's method of moments. Using the concept of cyclic invariant subspaces, conditions are studied that allow the generation of orthogonal Krylov subspace bases via short recurrences. The results motivate the important practical distinction between Hermitian and non-Hermitian problems. Finally, the book thoroughly addresses the computational cost while using Krylov subspace methods. The investigation includes effects of finite precision arithmetic andfocuses on the method of conjugate gradients (CG) and generalised minimal residuals (GMRES) as major examples.There is an emphasis on the way algebraic computations must always beconsidered in the context of solving real-world problems, where the mathematical modelling, discretisation and computation cannot be separated from each other. The book also underlines the importance of the historical context and demonstrates that knowledge of early developments can play an important role in understanding and resolving very recent computational problems. Many extensive historical notes are included as an inherent part of the text as well as the formulation of some omittedissues and challenges which need to be addressed in future work.This book is applicable to a wide variety of graduate courses on Krylov subspace methods and related subjects, as wellas benefiting those interested in the history of mathematics. Describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods, challenging some common assumptions and justifications of standard approaches. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.…