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Fast Algorithms For Structured Matrices
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Book Synopsis Fast Reliable Algorithms for Matrices with Structure by : T. Kailath
Download or read book Fast Reliable Algorithms for Matrices with Structure written by T. Kailath and published by SIAM. This book was released on 1999-01-01 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the combined issues of speed and numerical reliability in algorithm development.
Book Synopsis Structured Matrices and Polynomials by : Victor Y. Pan
Download or read book Structured Matrices and Polynomials written by Victor Y. Pan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This user-friendly, engaging textbook makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. The book goes beyond research frontiers and, apart from very recent research articles, includes previously unpublished results.
Book Synopsis Fast Algorithms for Structured Matrices by : Vadim Olshevsky
Download or read book Fast Algorithms for Structured Matrices written by Vadim Olshevsky and published by American Mathematical Soc.. This book was released on 2003 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered, and the theory of structured matrices emerged. This volume contains 22 survey and research papers devoted to a variety of theoretical and practical aspects of the design of fast algorithms for structured matrices and related issues. Included are several papers containing various affirmative and negative results in this direction. The theory of rational interpolation is one of the excellent sources providing intuition and methods to design fast algorithms. The volume contains several computational and theoretical papers on the topic. There are several papers on new applications of structured matrices, e.g., to the design of fast decoding algorithms, computing state-space realizations, relations to Lie algebras, unconstrained optimization, solving matrix equations, etc. The book is suitable for mathematicians, engineers, and numerical analysts who design, study, and use fast computational algorithms based on the theory of structured matrices.
Author :Vadim Olshevsky Publisher :Society for Industrial and Applied Mathematics ISBN 13 :9780898715439 Total Pages :440 pages Book Rating :4.7/5 (154 download)
Book Synopsis Fast Algorithms for Structured Matrices by : Vadim Olshevsky
Download or read book Fast Algorithms for Structured Matrices written by Vadim Olshevsky and published by Society for Industrial and Applied Mathematics. This book was released on 1987-01-01 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: AMS-IMS-SIAM Joint Summer Research Conference Papers on Fast Algorithms in Mathematics, Computer Science and Engineering. Held August 5-9, 2001 at Mount Holyoke College, South Hadley, Massachusetts.
Book Synopsis Fast Reliable Algorithms for Matrices with Structure by : T. Kailath
Download or read book Fast Reliable Algorithms for Matrices with Structure written by T. Kailath and published by SIAM. This book was released on 1999-01-01 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to pay special attention to the combined issues of speed and numerical reliability in algorithm development. These two requirements have often been regarded as competitive, so much so that the design of fast and numerically reliable algorithms for large-scale structured systems of linear equations, in many cases, remains a significant open issue. Fast Reliable Algorithms for Matrices with Structure helps bridge this gap by providing the reader with recent contributions written by leading experts in the field. The authors deal with both the theory and the practice of fast numerical algorithms for large-scale structured linear systems. Each chapter covers in detail different aspects of the most recent trends in the theory of fast algorithms, with emphasis on implementation and application issues. Both direct and iterative methods are covered. This book is not merely a collection of articles. The editors have gone to considerable lengths to blend the individual papers into a consistent presentation. Each chapter exposes the reader to some of the most recent research while providing enough background material to put the work into proper context.
Book Synopsis High Performance Algorithms for Structured Matrix Problems by : Peter Arbenz
Download or read book High Performance Algorithms for Structured Matrix Problems written by Peter Arbenz and published by Nova Publishers. This book was released on 1998 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprises 10 contributions that summarize the state of the art in the areas of high performance solutions of structured linear systems and structured eigenvalue and singular-value problems. Topics covered range from parallel solvers for sparse or banded linear systems to parallel computation of eigenvalues and singular values of tridiagonal and bidiagonal matrices. Specific paper topics include: the stable parallel solution of general narrow banded linear systems; efficient algorithms for reducing banded matrices to bidiagonal and tridiagonal form; a numerical comparison of look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems; and parallel CG-methods automatically optimized for PC and workstation clusters. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Separable Type Representations of Matrices and Fast Algorithms by : Yuli Eidelman
Download or read book Separable Type Representations of Matrices and Fast Algorithms written by Yuli Eidelman and published by Springer Science & Business Media. This book was released on 2013-10-08 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The main attention is paid to fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work is focused on algorithms of multiplication, inversion and description of eigenstructure and includes a large number of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is of a mainly theoretical character introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part contains factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structure. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and the accessible style the text will be useful to engineers, scientists, numerical analysts, computer scientists and mathematicians alike.
Book Synopsis Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications by : Michele Benzi
Download or read book Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications written by Michele Benzi and published by Springer. This book was released on 2017-01-24 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.
Book Synopsis Fast Direct Solvers for Elliptic PDEs by : Per-Gunnar Martinsson
Download or read book Fast Direct Solvers for Elliptic PDEs written by Per-Gunnar Martinsson and published by SIAM. This book was released on 2019-12-16 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.
Book Synopsis Structured Matrices in Mathematics, Computer Science, and Engineering I by : Vadim Olshevsky
Download or read book Structured Matrices in Mathematics, Computer Science, and Engineering I written by Vadim Olshevsky and published by American Mathematical Soc.. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Linear Algebra by : Leslie Hogben
Download or read book Handbook of Linear Algebra written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1838 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and
Book Synopsis Structured Matrices in Mathematics, Computer Science, and Engineering II by : Vadim Olshevsky
Download or read book Structured Matrices in Mathematics, Computer Science, and Engineering II written by Vadim Olshevsky and published by American Mathematical Soc.. This book was released on 2001 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numberical issues. The presentation fully illustrates the fact that the technicques of engineers, mathematicisn, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices"--Back cover.
Book Synopsis Numerical Methods for Structured Matrices and Applications by : Dario Andrea Bini
Download or read book Numerical Methods for Structured Matrices and Applications written by Dario Andrea Bini and published by Springer Science & Business Media. This book was released on 2011-02-09 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to topics such as fast algorithms, in which the late Georg Heinig made outstanding achievements.
Book Synopsis Structured Matrix Based Methods for Approximate Polynomial GCD by : Paola Boito
Download or read book Structured Matrix Based Methods for Approximate Polynomial GCD written by Paola Boito and published by Springer Science & Business Media. This book was released on 2012-03-13 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial computations, the polynomial GCD problem can be expressed in matrix form: the second part of the book focuses on this point of view and analyses the structure of the relevant matrices, such as Toeplitz, Toepliz-block and displacement structures. New algorithms for the computation of approximate polynomial GCD are presented, along with extensive numerical tests. The use of matrix structure allows, in particular, to lower the asymptotic computational cost from cubic to quadratic order with respect to polynomial degree.
Book Synopsis Structured Matrices in Mathematics, Computer Science, and Engineering by : Vadim Olshevsky
Download or read book Structured Matrices in Mathematics, Computer Science, and Engineering written by Vadim Olshevsky and published by American Mathematical Soc.. This book was released on 2001-09-14 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many important problems in applied sciences, mathematics, and engineering can be reduced to matrix problems. Moreover, various applications often introduce a special structure into the corresponding matrices, so that their entries can be described by a certain compact formula. Classic examples include Toeplitz matrices, Hankel matrices, Vandermonde matrices, Cauchy matrices, Pick matrices, Bezoutians, controllability and observability matrices, and others. Exploiting these and the more general structures often allows us to obtain elegant solutions to mathematical problems as well as to design more efficient practical algorithms for a variety of applied engineering problems. Structured matrices have been under close study for a long time and in quite diverse (and seemingly unrelated) areas, for example, mathematics, computer science, and engineering. Considerable progress has recently been made in all these areas, and especially in studying the relevant numerical and computational issues. In the past few years, a number of practical algorithms blending speed and accuracy have been developed. This significant growth is fully reflected in these volumes, which collect 38 papers devoted to the numerous aspects of the topic. The collection of the contributions to these volumes offers a flavor of the plethora of different approaches to attack structured matrix problems. The reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, as well as computational and numerical issues. The presentation fully illustrates the fact that the techniques of engineers, mathematicians, and numerical analysts nicely complement each other, and they all contribute to one unified theory of structured matrices. The book is published in two volumes. The first contains articles on interpolation, system theory, signal and image processing, control theory, and spectral theory. Articles in the second volume are devoted to fast algorithms, numerical and iterative methods, and various applications.
Book Synopsis Hierarchical Matrices: Algorithms and Analysis by : Wolfgang Hackbusch
Download or read book Hierarchical Matrices: Algorithms and Analysis written by Wolfgang Hackbusch and published by Springer. This book was released on 2015-12-21 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.
Book Synopsis Matrix Computations and Semiseparable Matrices by : Raf Vandebril
Download or read book Matrix Computations and Semiseparable Matrices written by Raf Vandebril and published by JHU Press. This book was released on 2008-01-14 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.
