Advances in Numerical Methods for Large Sparse Sets of Linear Equations PDF Download

Author:
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ISBN:
Category :
Languages : en
Pages :

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Author: Makoto Natori
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 64

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Author: Yousef Saad
Publisher: SIAM
ISBN: 0898715342
Category : Mathematics
Languages : en
Pages : 537

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Mathematics of Computing -- General.

Author: Takeshi Nodera
Publisher:
ISBN:
Category : Conjugate gradient methods
Languages : en
Pages : 78

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Author: Gerard Meurant
Publisher: Elsevier
ISBN: 0080529518
Category : Mathematics
Languages : en
Pages : 777

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Book Description
This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.

Author: Larisa Beilina
Publisher: Springer
ISBN: 3319573047
Category : Mathematics
Languages : en
Pages : 459

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This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigenproblems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

Author: Yousef Saad
Publisher: SIAM
ISBN: 9780898718003
Category : Mathematics
Languages : en
Pages : 546

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Since the first edition of this book was published in 1996, tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of the new generation of linear and nonlinear systems arising in typical applications has grown. Solving the three-dimensional models of these problems using direct solvers is no longer effective. At the same time, parallel computing has penetrated these application areas as it became less expensive and standardized. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. Iterative Methods for Sparse Linear Systems, Second Edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.

Author: Daniele Bertaccini
Publisher: CRC Press
ISBN: 1351649612
Category : Mathematics
Languages : en
Pages : 321

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This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.

Author: Yousef Saad
Publisher: SIAM
ISBN: 9781611970739
Category : Mathematics
Languages : en
Pages : 292

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Book Description
This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

Author: Makoto Natori
Publisher:
ISBN:
Category : Conjugate gradient methods
Languages : ja
Pages : 122

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