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Iterative Methods for Linear Systems

2014-07-21 Mathematics
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Release : 2014-07-21
Genre : Mathematics
Kind : eBook
Book Rating : 465/5 ( reviews)

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Book Synopsis Iterative Methods for Linear Systems by : Maxim A. Olshanskii

Download or read book Iterative Methods for Linear Systems written by Maxim A. Olshanskii. This book was released on 2014-07-21. Available in PDF, EPUB and Kindle. Book excerpt: Iterative Methods for Linear Systems?offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.??

Iterative Methods for Sparse Linear Systems

2003-04-01 Mathematics
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Release : 2003-04-01
Genre : Mathematics
Kind : eBook
Book Rating : 342/5 ( reviews)

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Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad. This book was released on 2003-04-01. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Iterative Methods for Solving Linear Systems

1997-01-01 Mathematics
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Release : 1997-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 96X/5 ( reviews)

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Book Synopsis Iterative Methods for Solving Linear Systems by : Anne Greenbaum

Download or read book Iterative Methods for Solving Linear Systems written by Anne Greenbaum. This book was released on 1997-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Iterative Methods for Linear and Nonlinear Equations

1995-01-01 Mathematics
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Release : 1995-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 944/5 ( reviews)

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Book Synopsis Iterative Methods for Linear and Nonlinear Equations by : C. T. Kelley

Download or read book Iterative Methods for Linear and Nonlinear Equations written by C. T. Kelley. This book was released on 1995-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.

Iterative Methods and Preconditioners for Systems of Linear Equations

2022-02-08 Mathematics
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Release : 2022-02-08
Genre : Mathematics
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Book Rating : 901/5 ( reviews)

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Book Synopsis Iterative Methods and Preconditioners for Systems of Linear Equations by : Gabriele Ciaramella

Download or read book Iterative Methods and Preconditioners for Systems of Linear Equations written by Gabriele Ciaramella. This book was released on 2022-02-08. Available in PDF, EPUB and Kindle. Book excerpt: Iterative methods use successive approximations to obtain more accurate solutions. This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations and optimal control problems governed by the Laplace equation, for which the use of matrix-free procedures is crucial. All methods are explained and analyzed starting from the historical ideas of the inventors, which are often quoted from their seminal works. Iterative Methods and Preconditioners for Systems of Linear Equations grew out of a set of lecture notes that were improved and enriched over time, resulting in a clear focus for the teaching methodology, which derives complete convergence estimates for all methods, illustrates and provides MATLAB codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students who want an overview or deeper understanding of iterative methods. Its focus on both analysis and numerical experiments allows the material to be taught with very little preparation, since all the arguments are self-contained, and makes it appropriate for self-study as well. It can be used in courses on iterative methods, Krylov methods and preconditioners, and numerical optimal control. Scientists and engineers interested in new topics and applications will also find the text useful.

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