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Structured Matrices and Polynomials

Structured Matrices and Polynomials Author Victor Y. Pan
ISBN-10 9781461201298
Release 2012-12-06
Pages 278
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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 The book goes beyond research frontiers and, apart from very recent research articles, includes previously unpublished results.



Structured Matrix Based Methods for Approximate Polynomial GCD

Structured Matrix Based Methods for Approximate Polynomial GCD Author Paola Boito
ISBN-10 9788876423819
Release 2012-03-13
Pages 250
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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.



Algorithms and Theory of Computation Handbook Second Edition Volume 1

Algorithms and Theory of Computation Handbook  Second Edition  Volume 1 Author Mikhail J. Atallah
ISBN-10 1584888237
Release 2009-11-20
Pages 988
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Algorithms and Theory of Computation Handbook, Second Edition: General Concepts and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. Along with updating and revising many of the existing chapters, this second edition contains four new chapters that cover external memory and parameterized algorithms as well as computational number theory and algorithmic coding theory. This best-selling handbook continues to help computer professionals and engineers find significant information on various algorithmic topics. The expert contributors clearly define the terminology, present basic results and techniques, and offer a number of current references to the in-depth literature. They also provide a glimpse of the major research issues concerning the relevant topics.



Numerical Methods for Structured Matrices and Applications

Numerical Methods for Structured Matrices and Applications Author Dario Andrea Bini
ISBN-10 3764389966
Release 2011-02-09
Pages 439
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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.



Matrix Computations and Semiseparable Matrices

Matrix Computations and Semiseparable Matrices Author Raf Vandebril
ISBN-10 0801887143
Release 2007-12-18
Pages 584
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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.



Octogon Mathematical Magazine

Octogon Mathematical Magazine Author
ISBN-10 UOM:39015057302294
Release 2002
Pages
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Octogon Mathematical Magazine has been writing in one form or another for most of life. You can find so many inspiration from Octogon Mathematical Magazine also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Octogon Mathematical Magazine book for free.



Structured Matrices

Structured Matrices Author Dario Bini
ISBN-10 1560728906
Release 2001-01-01
Pages 206
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Matrices with structure are encountered in a wide variety of problems in pure and applied mathematics, and in engineering. Matrix patterns and structural properties provide a uniform means for describing apparently different features of the problems that they model. This book collects a set of contributions in structured matrix computations that covers different facets of the problems involved in this research area. The book may be naturally divided into four parts: the first part contains two contributions on asymptotical spectral properties of structured matrices. The second part contains seven contributions related to algorithm design and analysts. The third part, consisting of three contributions, concerns issues specifically related to structures, algebras and polynomials. The fourth part concerns applications to image processing and differential equations.



Structured Eigenvalue Problems and Quadratic Eigenvalue Problems

Structured Eigenvalue Problems and Quadratic Eigenvalue Problems Author Jiang Zhu
ISBN-10 UCAL:C3504324
Release 2005
Pages 320
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Structured Eigenvalue Problems and Quadratic Eigenvalue Problems has been writing in one form or another for most of life. You can find so many inspiration from Structured Eigenvalue Problems and Quadratic Eigenvalue Problems also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Structured Eigenvalue Problems and Quadratic Eigenvalue Problems book for free.



International Mathematical News

International Mathematical News Author
ISBN-10 CORNELL:31924074908777
Release 2001
Pages
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Issues for Dec. 1952- include section: Nachrichten der √Ėsterreichischen Mathematischen Gesellschaft.



SIAM Journal on Computing

SIAM Journal on Computing Author Society for Industrial and Applied Mathematics
ISBN-10 UOM:39015058313928
Release 2002
Pages
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SIAM Journal on Computing has been writing in one form or another for most of life. You can find so many inspiration from SIAM Journal on Computing also informative, and entertaining. Click DOWNLOAD or Read Online button to get full SIAM Journal on Computing book for free.



Introduction to the Numerical Solution of Markov Chains

Introduction to the Numerical Solution of Markov Chains Author William J. Stewart
ISBN-10 9780691036991
Release 1994
Pages 539
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Markov chains; Direct methods; Iterative methods; Projection methods; Block hessenberg matrices and solution by recursion; decompositional methods; P-cyclic markov chains; Trasient solutions; Stochastic automata networks; Software; Bibliography; Index.



American Book Publishing Record

American Book Publishing Record Author
ISBN-10 STANFORD:36105111051640
Release 2001
Pages
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American Book Publishing Record has been writing in one form or another for most of life. You can find so many inspiration from American Book Publishing Record also informative, and entertaining. Click DOWNLOAD or Read Online button to get full American Book Publishing Record book for free.



Fast Reliable Algorithms for Matrices with Structure

Fast Reliable Algorithms for Matrices with Structure Author T. Kailath
ISBN-10 1611971357
Release 1999
Pages 342
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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.



Proceedings Annual Symposium on Foundations of Computer Science

Proceedings     Annual Symposium on Foundations of Computer Science Author
ISBN-10 UVA:X004278869
Release 1998
Pages
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Proceedings Annual Symposium on Foundations of Computer Science has been writing in one form or another for most of life. You can find so many inspiration from Proceedings Annual Symposium on Foundations of Computer Science also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Proceedings Annual Symposium on Foundations of Computer Science book for free.



Structured Matrices in Mathematics Computer Science and Engineering

Structured Matrices in Mathematics  Computer Science  and Engineering Author Vadim Olshevsky
ISBN-10 9780821820926
Release 2001
Pages 344
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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.



Tellegen s Theorem and Electrical Networks

Tellegen s Theorem and Electrical Networks Author Paul Penfield
ISBN-10 WISC:89042728857
Release 1970
Pages 143
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B. D. H. Tellegen's theorem is still not as widely known as its utility warrants. The authors of this monograph set out to correct this neglect.



Accuracy and Stability of Numerical Algorithms

Accuracy and Stability of Numerical Algorithms Author Nicholas J. Higham
ISBN-10 0898718023
Release 2002
Pages 680
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Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.