Matrix Inequalities For Iterative Systems

Author : Hanjo Taubig
Publisher : CRC Press
ISBN 13 : 1351679090
Total Pages : 144 pages
Book Rating : 4.91/5 ( download)

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Download or read book Matrix Inequalities for Iterative Systems written by Hanjo Taubig and published by CRC Press. This book was released on 2017-02-03 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.

Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.47/5 ( download)

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Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Author : Laurent El Ghaoui
Publisher : SIAM
ISBN 13 : 0898714389
Total Pages : 371 pages
Book Rating : 4.88/5 ( download)

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Download or read book Advances in Linear Matrix Inequality Methods in Control written by Laurent El Ghaoui and published by SIAM. This book was released on 2000-01-01 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account of the LMI method, covering topics such as LMI algorithms, analysis and synthesis issues and nonconvex problems.

Author : Stephen Boyd
Publisher : SIAM
ISBN 13 : 9781611970777
Total Pages : 203 pages
Book Rating : 4.76/5 ( download)

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Download or read book Linear Matrix Inequalities in System and Control Theory written by Stephen Boyd and published by SIAM. This book was released on 1994-01-01 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors reduce a wide variety of problems arising in system and control theory to a handful of convex and quasiconvex optimization problems that involve linear matrix inequalities. These optimization problems can be solved using recently developed numerical algorithms that not only are polynomial-time but also work very well in practice; the reduction therefore can be considered a solution to the original problems. This book opens up an important new research area in which convex optimization is combined with system and control theory, resulting in the solution of a large number of previously unsolved problems.

Author : Dominique Orban
Publisher : SIAM
ISBN 13 : 1611974739
Total Pages : 93 pages
Book Rating : 4.37/5 ( download)

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Download or read book Iterative Solution of Symmetric Quasi-definite Linear Systems written by Dominique Orban and published by SIAM. This book was released on 2017-04-07 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous applications, including computational optimization and fluid dynamics, give rise to block linear systems of equations said to have the quasi-definite structure. In practical situations, the size or density of those systems can preclude a factorization approach, leaving only iterative methods as the solution technique. Known iterative methods, however, are not specifically designed to take advantage of the quasi-definite structure.÷ This book discusses the connection between quasi-definite systems and linear least-squares problems, the most common and best understood problems in applied mathematics, and explains how quasi-definite systems can be solved using tailored iterative methods for linear least squares (with half as much work!). To encourage researchers and students to use the software, it is provided in MATLAB, Python, and Julia.÷ The authors provide a concise account of the most well-known methods for symmetric systems and least-squares problems, research-level advances in the solution of problems with specific illustrations in optimization and fluid dynamics, and a website that hosts software in three languages.÷

Author : Maxim A. Olshanskii
Publisher : SIAM
ISBN 13 : 1611973465
Total Pages : 257 pages
Book Rating : 4.64/5 ( download)

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Download or read book Iterative Methods for Linear Systems written by Maxim A. Olshanskii and published by SIAM. This book was released on 2014-07-21 with total page 257 pages. 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.??

Author : Richard S. Varga
Publisher : Springer Science & Business Media
ISBN 13 : 3642051545
Total Pages : 362 pages
Book Rating : 4.48/5 ( download)

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Download or read book Matrix Iterative Analysis written by Richard S. Varga and published by Springer Science & Business Media. This book was released on 2009-12-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.

Author : Anne Greenbaum
Publisher : SIAM
ISBN 13 : 089871396X
Total Pages : 225 pages
Book Rating : 4.61/5 ( download)

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Download or read book Iterative Methods for Solving Linear Systems written by Anne Greenbaum and published by SIAM. This book was released on 1997-01-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Author : Wolfgang Hackbusch
Publisher : Springer
ISBN 13 : 3319284835
Total Pages : 528 pages
Book Rating : 4.35/5 ( download)

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Download or read book Iterative Solution of Large Sparse Systems of Equations written by Wolfgang Hackbusch and published by Springer. This book was released on 2016-06-21 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.

Author : David M. Young
Publisher : Courier Corporation
ISBN 13 : 0486153339
Total Pages : 612 pages
Book Rating : 4.39/5 ( download)

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Download or read book Iterative Solution of Large Linear Systems written by David M. Young and published by Courier Corporation. This book was released on 2013-07-24 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes a review of matrix theory and iterative methods; successive overrelaxation (SOR) method and stationary modified SOR method for consistently ordered matrices; nonstationary methods; generalizations of SOR theory and variants of method; more. 1971 edition.