Polynomial And Matrix Computations Fundamental Algorithms
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Polynomial And Matrix Computations
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Author : Dario Bini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Polynomial And Matrix Computations written by Dario Bini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Polynomial And Matrix Computations Fundamental Algorithms
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Author : Dario Bini
language : en
Publisher:
Release Date : 1994
Polynomial And Matrix Computations Fundamental Algorithms written by Dario Bini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Matrices categories.
Exploiting Hidden Structure In Matrix Computations Algorithms And Applications
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Author : Michele Benzi
language : en
Publisher: Springer
Release Date : 2017-01-24
Exploiting Hidden Structure In Matrix Computations Algorithms And Applications written by Michele Benzi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Mathematics categories.
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.
Algorithms And Theory Of Computation Handbook Volume 1
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Author : Mikhail J. Atallah
language : en
Publisher: CRC Press
Release Date : 2009-11-20
Algorithms And Theory Of Computation Handbook Volume 1 written by Mikhail J. Atallah and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-20 with Computers categories.
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
Algorithms And Theory Of Computation Handbook 2 Volume Set
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Author : Mikhail J. Atallah
language : en
Publisher: CRC Press
Release Date : 2022-05-29
Algorithms And Theory Of Computation Handbook 2 Volume Set written by Mikhail J. Atallah and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-29 with Computers categories.
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
Numerical Methods For Roots Of Polynomials Part Ii
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Author : J.M. McNamee
language : en
Publisher: Elsevier Inc. Chapters
Release Date : 2013-07-19
Numerical Methods For Roots Of Polynomials Part Ii written by J.M. McNamee and has been published by Elsevier Inc. Chapters this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-19 with Mathematics categories.
The zeros of a polynomial can be readily recovered from its linear factors. The linear factors can be approximated by first splitting a polynomial numerically into the product of its two nonconstant factors and then recursively splitting every computed nonlinear factor in similar fashion. For both the worst and average case inputs the resulting algorithms solve the polynomial factorization and root-finding problems within fixed sufficiently small error bounds by using nearly optimal arithmetic and Boolean time, that is using nearly optimal numbers of arithmetic and bitwise operations; in the case of a polynomial with integer coefficients and simple roots we can immediately extend factorization to root isolation, that is to computing disjoint covering discs, one for every root on the complex plane. The presented algorithms compute highly accurate approximations to all roots nearly as fast as one reads the input coefficients. Furthermore, our algorithms allow processor efficient parallel acceleration, which enables root-finding, factorization, and root isolation in polylogarithmic arithmetic and Boolean time. The chapter thoroughly covers the design and analysis of these algorithms, including auxiliary techniques of independent interest. At the end we compare the presented polynomial root-finders with alternative ones, in particular with the popular algorithms adopted by users based on supporting empirical information. We also comment on some promising directions to further progress.
Encyclopedia Of Computer Science And Technology
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Author : Allen Kent
language : en
Publisher: CRC Press
Release Date : 2021-06-23
Encyclopedia Of Computer Science And Technology written by Allen Kent and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-23 with Computers categories.
Volume 39 - Supplement 24 - Entity Identification to Virtual Reality in Driving Simulation. Covering more than basic computer commands and procedures, this encyclopaedia summarizes how technology has developed, the future of computer programs and applications, and the significance of computer components. Following an introduction and overview, there are approximately 750 to 800 entries.
Fast Matrix Multiplication With Applications
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Author : Jerzy S. Respondek
language : en
Publisher: Springer Nature
Release Date : 2025-02-26
Fast Matrix Multiplication With Applications written by Jerzy S. Respondek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-26 with Computers categories.
The ambition of this monograph is to show the methods of constructing fast matrix multiplication algorithms, and their applications, in an intelligible way, accessible not only to mathematicians. The scope and coverage of the book are comprehensive and constructive, and the analyses and algorithms can be readily applied by readers from various disciplines of science and technology who need modern tools and techniques related to fast matrix multiplication and related problems and techniques. Authors start from commutative algorithms, through exact non-commutative algorithms, partial algorithms to disjoint and arbitrary precision algorithms. Authors explain how to adapt disjoint algorithms to a single matrix multiplication and prove the famous tau-theorem in the (not so) special case. In an appendix, authors show how to work with confluent Vandermonde matrices, since they are used as an auxiliary tool in problems arising in fast matrix multiplication. Importantly, each algorithm is demonstrated by a concrete example of a decent dimensionality to ensure that all the mechanisms of the algorithms are illustrated. Finally, authors give a series of applications of fast matrix multiplication algorithms in linear algebra and other types of problems, including artificial intelligence.
Foundations Of Computational Mathematics
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Author : Felipe Cucker
language : en
Publisher: World Scientific
Release Date : 2002
Foundations Of Computational Mathematics written by Felipe Cucker and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This invaluable book contains 19 papers selected from those submitted to a conference held in Hong Kong in July 2000 to celebrate the 70th birthday of Professor Steve Smale. It may be regarded as a continuation of the proceedings of SMALEFEST 1990 ("From Topology to Computation") held in Berkeley, USA, 10 years before, but with the focus on the area in which Smale worked more intensively during the '90's, namely the foundations of computational mathematics.
Computational Methods For Physicists
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Author : Simon Sirca
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-17
Computational Methods For Physicists written by Simon Sirca and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-17 with Science categories.
This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.