Error Free Polynomial Matrix Computations

Author : E.V. Krishnamurthy
Publisher : Springer Science & Business Media
ISBN 13 : 1461251184
Total Pages : 170 pages
Book Rating : 4.87/5 ( download)

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Download or read book Error-Free Polynomial Matrix Computations written by E.V. Krishnamurthy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as an introduction to polynomial matrix computa tions. It is a companion volume to an earlier book on Methods and Applications of Error-Free Computation by R. T. Gregory and myself, published by Springer-Verlag, New York, 1984. This book is intended for seniors and graduate students in computer and system sciences, and mathematics, and for researchers in the fields of computer science, numerical analysis, systems theory, and computer algebra. Chapter I introduces the basic concepts of abstract algebra, including power series and polynomials. This chapter is essentially meant for bridging the gap between the abstract algebra and polynomial matrix computations. Chapter II is concerned with the evaluation and interpolation of polynomials. The use of these techniques for exact inversion of poly nomial matrices is explained in the light of currently available error-free computation methods. In Chapter III, the principles and practice of Fourier evaluation and interpolation are described. In particular, the application of error-free discrete Fourier transforms for polynomial matrix computations is consi dered.

Author : Dario Bini
Publisher : Springer Science & Business Media
ISBN 13 : 1461202655
Total Pages : 433 pages
Book Rating : 4.53/5 ( download)

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Download or read book Polynomial and Matrix Computations written by Dario Bini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our Subjects and Objectives. This book is about algebraic and symbolic computation and numerical computing (with matrices and polynomials). It greatly extends the study of these topics presented in the celebrated books of the seventies, [AHU] and [BM] (these topics have been under-represented in [CLR], which is a highly successful extension and updating of [AHU] otherwise). Compared to [AHU] and [BM] our volume adds extensive material on parallel com putations with general matrices and polynomials, on the bit-complexity of arithmetic computations (including some recent techniques of data compres sion and the study of numerical approximation properties of polynomial and matrix algorithms), and on computations with Toeplitz matrices and other dense structured matrices. The latter subject should attract people working in numerous areas of application (in particular, coding, signal processing, control, algebraic computing and partial differential equations). The au thors' teaching experience at the Graduate Center of the City University of New York and at the University of Pisa suggests that the book may serve as a text for advanced graduate students in mathematics and computer science who have some knowledge of algorithm design and wish to enter the exciting area of algebraic and numerical computing. The potential readership may also include algorithm and software designers and researchers specializing in the design and analysis of algorithms, computational complexity, alge braic and symbolic computing, and numerical computation.

Author : Dario Bini
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.54/5 ( download)

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Download or read book Polynomial and Matrix Computations written by Dario Bini and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : R. T. Gregory
Publisher : Springer Science & Business Media
ISBN 13 : 1461252423
Total Pages : 204 pages
Book Rating : 4.29/5 ( download)

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Download or read book Methods and Applications of Error-Free Computation written by R. T. Gregory and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as an introduction to the theory of error-free computation. In addition, we include several chapters that illustrate how error-free com putation can be applied in practice. The book is intended for seniors and first year graduate students in fields of study involving scientific computation using digital computers, and for researchers (in those same fields) who wish to obtain an introduction to the subject. We are motivated by the fact that there are large classes of ill-conditioned problems, and there are numerically unstable algorithms, and in either or both of these situations we cannot tolerate rounding errors during the numerical computations involved in obtaining solutions to the problems. Thus, it is important to study finite number systems for digital computers which have the property that computation can be performed free of rounding errors. In Chapter I we discuss single-modulus and multiple-modulus residue number systems and arithmetic in these systems, where the operands may be either integers or rational numbers. In Chapter II we discuss finite-segment p-adic number systems and their relationship to the p-adic numbers of Hensel [1908]. Each rational number in a certain finite set is assigned a unique Hensel code and arithmetic operations using Hensel codes as operands is mathe matically equivalent to those same arithmetic operations using the cor responding rational numbers as operands. Finite-segment p-adic arithmetic shares with residue arithmetic the property that it is free of rounding errors.

Author : John Rischard Rice
Publisher : McGraw-Hill Companies
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.92/5 ( download)

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Download or read book Matrix Computations and Mathematical Software written by John Rischard Rice and published by McGraw-Hill Companies. This book was released on 1981 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra background; types and sources of matrix computational problems; type of matrix that arise; gauss elimination and LU factorization; mathematical software objectives; mathematical software performance evaluation; how do you know you have right answers?; conditioning and backward error analysis; iterative methods; linear least squares and regression; projects; standard linear algebra software.

Author : Jens Volkert
Publisher : Springer Science & Business Media
ISBN 13 : 9783540573142
Total Pages : 268 pages
Book Rating : 4.43/5 ( download)

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Download or read book Parallel Computation written by Jens Volkert and published by Springer Science & Business Media. This book was released on 1993-09-27 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Austrian Center for Parallel Computation (ACPC) is a cooperative research organization founded in 1989 to promote research and education in the field of software for parallel computer systems. The areas in which the ACPC is active include algorithms, languages, compilers, programming environments, and applications for parallel and high-performance computing systems. This volume contains the proceedings of the Second International Conference of the ACPC, held in Gmunden, Austria, October 1993. Authors from 17 countries submitted 44 papers, of which 15 were selected for inclusion in this volume, which also includes 4 invited papers by distinguished researchers. The volume is organized into parts on architectures (2 papers), algorithms (7 papers), languages (6 papers), and programming environments (4 papers).

Author : Alfonso Miola
Publisher : Springer Science & Business Media
ISBN 13 : 3709165318
Total Pages : 270 pages
Book Rating : 4.17/5 ( download)

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Download or read book Advances in the Design of Symbolic Computation Systems written by Alfonso Miola and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: New methodological aspects related to design and implementation of symbolic computation systems are considered in this volume aiming at integrating such aspects into a homogeneous software environment for scientific computation. The proposed methodology is based on a combination of different techniques: algebraic specification through modular approach and completion algorithms, approximated and exact algebraic computing methods, object-oriented programming paradigm, automated theorem proving through methods à la Hilbert and methods of natural deduction. In particular the proposed treatment of mathematical objects, via techniques for method abstraction, structures classification, and exact representation, the programming methodology which supports the design and implementation issues, and reasoning capabilities supported by the whole framework are described.

Author : Mikhail J. Atallah
Publisher : CRC Press
ISBN 13 : 1439832331
Total Pages : 1944 pages
Book Rating : 4.32/5 ( download)

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Download or read book Algorithms and Theory of Computation Handbook - 2 Volume Set written by Mikhail J. Atallah and published by CRC Press. This book was released on 2022-05-30 with total page 1944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms and Theory of Computation Handbook, Second Edition in a two volume set, 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. New to the Second Edition: Along with updating and revising many of the existing chapters, this second edition contains more than 20 new chapters. This edition now covers external memory, parameterized, self-stabilizing, and pricing algorithms as well as the theories of algorithmic coding, privacy and anonymity, databases, computational games, and communication networks. It also discusses computational topology, computational number theory, natural language processing, and grid computing and explores applications in intensity-modulated radiation therapy, voting, DNA research, systems biology, and financial derivatives. 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

Author : Athanasios C. Antoulas
Publisher : Springer Science & Business Media
ISBN 13 : 3662085461
Total Pages : 589 pages
Book Rating : 4.62/5 ( download)

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Download or read book Mathematical System Theory written by Athanasios C. Antoulas and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past three decades R.E. Kalman has been one of the most influential personalities in system and control theory. His ideas have been instrumental in a variety of areas. This is a Festschrift honoring his 60th birthday. It contains contributions from leading researchers in the field giving an account of the profound influence of his ideas in a number of areas of active research in system and control theory. For example, since their introduction by Kalman in the early 60's, the concepts of controllability and observability of dynamical systems with inputs, have been the corner stone of the great majority of investigations in the field.

Author : Peter M.A. Sloot
Publisher : Springer
ISBN 13 : 3540448640
Total Pages : 1188 pages
Book Rating : 4.48/5 ( download)

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Download or read book Computational Science — ICCS 2003 written by Peter M.A. Sloot and published by Springer. This book was released on 2003-08-03 with total page 1188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-volume set LNCS 2657, LNCS 2658, LNCS 2659, and LNCS 2660 constitutes the refereed proceedings of the Third International Conference on Computational Science, ICCS 2003, held concurrently in Melbourne, Australia and in St. Petersburg, Russia in June 2003. The four volumes present more than 460 reviewed contributed and invited papers and span the whole range of computational science, from foundational issues in computer science and algorithmic mathematics to advanced applications in virtually all application fields making use of computational techniques. These proceedings give a unique account of recent results in the field.