Incomplete Factorization Preconditioning for Linear Least Squares Problems

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Publisher :
ISBN 13 :
Total Pages : 218 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Incomplete Factorization Preconditioning for Linear Least Squares Problems by : Xiaoge Wang

Download or read book Incomplete Factorization Preconditioning for Linear Least Squares Problems written by Xiaoge Wang and published by . This book was released on 1993 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: When certain conditions are imposed on the sparsity pattern of the preconditioning matrix, incomplete Cholesky (IC) factorization is identical to IMGS. Therefore, a sufficient condition on the sparsity pattern for a stable IC factorization can be derived. Based on this condition, three algorithms for modifying a sparsity pattern for which IC may not succeed have been designed. These methods differ from previously proposed methods to guarantee the existence and improve the stability of the IC factorization since they do not require numerical information. Numerical experiments illustrating the capabilities of the preconditioners are also presented."

Numerical Methods for Least Squares Problems, Second Edition

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Publisher : SIAM
ISBN 13 : 1611977959
Total Pages : 509 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Numerical Methods for Least Squares Problems, Second Edition by : Åke Björck

Download or read book Numerical Methods for Least Squares Problems, Second Edition written by Åke Björck and published by SIAM. This book was released on 2024-07-05 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares, discovered by Gauss in 1795, is a principal tool for reducing the influence of errors when fitting a mathematical model to given observations. Applications arise in many areas of science and engineering. The increased use of automatic data capturing frequently leads to large-scale least squares problems. Such problems can be solved by using recent developments in preconditioned iterative methods and in sparse QR factorization. The first edition of Numerical Methods for Least Squares Problems was the leading reference on the topic for many years. The updated second edition stands out compared to other books on this subject because it provides an in-depth and up-to-date treatment of direct and iterative methods for solving different types of least squares problems and for computing the singular value decomposition. It also is unique because it covers generalized, constrained, and nonlinear least squares problems as well as partial least squares and regularization methods for discrete ill-posed problems. The bibliography of over 1,100 historical and recent references provides a comprehensive survey of past and present research in the field. This book will be of interest to graduate students and researchers in applied mathematics and to researchers working with numerical linear algebra applications.

Numerical Methods for Least Squares Problems

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Publisher : SIAM
ISBN 13 : 9781611971484
Total Pages : 425 pages
Book Rating : 4.9/5 (714 download)

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Book Synopsis Numerical Methods for Least Squares Problems by : Ake Bjorck

Download or read book Numerical Methods for Least Squares Problems written by Ake Bjorck and published by SIAM. This book was released on 1996-01-01 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.

Robust Preconditioners for Large Sparse Linear Systems and Least-squares Problems

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Publisher :
ISBN 13 :
Total Pages : 370 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Robust Preconditioners for Large Sparse Linear Systems and Least-squares Problems by : Na Li

Download or read book Robust Preconditioners for Large Sparse Linear Systems and Least-squares Problems written by Na Li and published by . This book was released on 2006 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Survey of Preconditioned Iterative Methods

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Publisher : Routledge
ISBN 13 : 1351469363
Total Pages : 180 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis A Survey of Preconditioned Iterative Methods by : Are Magnus Bruaset

Download or read book A Survey of Preconditioned Iterative Methods written by Are Magnus Bruaset and published by Routledge. This book was released on 2018-12-13 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w

Numerical Analysis and Its Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540625988
Total Pages : 628 pages
Book Rating : 4.6/5 (259 download)

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Book Synopsis Numerical Analysis and Its Applications by : Lubin Vulkov

Download or read book Numerical Analysis and Its Applications written by Lubin Vulkov and published by Springer Science & Business Media. This book was released on 1997-02-26 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First International Workshop on Numerical Analysis and Its Applications, WNAA'96, held in Rousse, Bulgaria, in June 1996. The 57 revised full papers presented were carefully selected and reviewed for inclusion in the volume; also included are 14 invited presentations. All in all, the book offers a wealth of new results and methods of numerical analysis applicable in computational science, particularly in computational physics and chemistry. The volume reflects that the cooperation of computer scientists, mathematicians and scientists provides new numerical tools for computational scientists and, at the same time, stimulates numerical analysis.

Solving Nonlinear Equations with Newton's Method

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Publisher : SIAM
ISBN 13 : 9780898718898
Total Pages : 117 pages
Book Rating : 4.7/5 (188 download)

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Book Synopsis Solving Nonlinear Equations with Newton's Method by : C. T. Kelley

Download or read book Solving Nonlinear Equations with Newton's Method written by C. T. Kelley and published by SIAM. This book was released on 2003-01-01 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.

Parallel Processing and Applied Mathematics

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Publisher : Springer
ISBN 13 : 3319321498
Total Pages : 622 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Parallel Processing and Applied Mathematics by : Roman Wyrzykowski

Download or read book Parallel Processing and Applied Mathematics written by Roman Wyrzykowski and published by Springer. This book was released on 2016-04-05 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set LNCS 9573 and LNCS 9574 constitutes the refereed proceedings of the 11th International Conference of Parallel Processing and Applied Mathematics, PPAM 2015, held in Krakow, Poland, in September 2015.The 111 revised full papers presented in both volumes were carefully reviewed and selected from 196 submissions. The focus of PPAM 2015 was on models, algorithms, and software tools which facilitate efficient and convenient utilization of modern parallel and distributed computing architectures, as well as on large-scale applications, including big data problems.

Matrix Computations

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Publisher : JHU Press
ISBN 13 : 9780801854149
Total Pages : 734 pages
Book Rating : 4.8/5 (541 download)

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Book Synopsis Matrix Computations by : Gene H. Golub

Download or read book Matrix Computations written by Gene H. Golub and published by JHU Press. This book was released on 1996-10-15 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.

Direct Methods for Sparse Matrices

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Publisher : Oxford University Press
ISBN 13 : 0192507516
Total Pages : 539 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis Direct Methods for Sparse Matrices by : I. S. Duff

Download or read book Direct Methods for Sparse Matrices written by I. S. Duff and published by Oxford University Press. This book was released on 2017-02-10 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a million in the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done in the last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms. New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research of the authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.

Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications

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Publisher : CRC Press
ISBN 13 : 1351649612
Total Pages : 321 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications by : Daniele Bertaccini

Download or read book Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications written by Daniele Bertaccini and published by CRC Press. This book was released on 2018-02-19 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advances in Parallel & Distributed Processing, and Applications

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Publisher : Springer Nature
ISBN 13 : 3030699846
Total Pages : 1201 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Advances in Parallel & Distributed Processing, and Applications by : Hamid R. Arabnia

Download or read book Advances in Parallel & Distributed Processing, and Applications written by Hamid R. Arabnia and published by Springer Nature. This book was released on 2021-10-18 with total page 1201 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the proceedings of four conferences: The 26th International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA'20), The 18th International Conference on Scientific Computing (CSC'20); The 17th International Conference on Modeling, Simulation and Visualization Methods (MSV'20); and The 16th International Conference on Grid, Cloud, and Cluster Computing (GCC'20). The conferences took place in Las Vegas, NV, USA, July 27-30, 2020. The conferences are part of the larger 2020 World Congress in Computer Science, Computer Engineering, & Applied Computing (CSCE'20), which features 20 major tracks. Authors include academics, researchers, professionals, and students. Presents the proceedings of four conferences as part of the 2020 World Congress in Computer Science, Computer Engineering, & Applied Computing (CSCE'20); Includes the research tracks Parallel and Distributed Processing, Scientific Computing, Modeling, Simulation and Visualization, and Grid, Cloud, and Cluster Computing; Features papers from PDPTA’20, CSC’20, MSV’20, and GCC’20.

Matrix Analysis and Computations

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Publisher : SIAM
ISBN 13 : 1611976634
Total Pages : 496 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Matrix Analysis and Computations by : Zhong-Zhi Bai

Download or read book Matrix Analysis and Computations written by Zhong-Zhi Bai and published by SIAM. This book was released on 2021-09-09 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics

Iterative Methods for Sparse Linear Systems

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Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.8/5 (987 download)

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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 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.

Applied Parallel Computing. Computations in Physics, Chemistry and Engineering Science

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540609025
Total Pages : 582 pages
Book Rating : 4.6/5 (9 download)

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Book Synopsis Applied Parallel Computing. Computations in Physics, Chemistry and Engineering Science by : Jack Dongarra

Download or read book Applied Parallel Computing. Computations in Physics, Chemistry and Engineering Science written by Jack Dongarra and published by Springer Science & Business Media. This book was released on 1996-02-27 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the Second International Workshop on Applied Parallel Computing in Physics, Chemistry and Engineering Science, PARA'95, held in Lyngby, Denmark, in August 1995. The 60 revised full papers included have been contributed by physicists, chemists, and engineers, as well as by computer scientists and mathematicians, and document the successful cooperation of different scientific communities in the booming area of computational science and high performance computing. Many widely-used numerical algorithms and their applications on parallel computers are treated in detail.

Numerical Methods in Matrix Computations

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Publisher : Springer
ISBN 13 : 3319050893
Total Pages : 812 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Numerical Methods in Matrix Computations by : Åke Björck

Download or read book Numerical Methods in Matrix Computations written by Åke Björck and published by Springer. This book was released on 2014-10-07 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Iterative Methods for Linear and Nonlinear Equations

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Publisher : SIAM
ISBN 13 : 0898713528
Total Pages : 169 pages
Book Rating : 4.8/5 (987 download)

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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 and published by SIAM. This book was released on 1995-01-01 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.