Effective Polynomial Computation

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Effective Polynomial Computation

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Author : Richard Zippel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Effective Polynomial Computation written by Richard Zippel 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 Computers categories.

Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers). Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.

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.

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

Polynomial Algorithms In Computer Algebra

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Author : Franz Winkler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Polynomial Algorithms In Computer Algebra written by Franz Winkler 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.

For several years now I have been teaching courses in computer algebra at the Universitat Linz, the University of Delaware, and the Universidad de Alcala de Henares. In the summers of 1990 and 1992 I have organized and taught summer schools in computer algebra at the Universitat Linz. Gradually a set of course notes has emerged from these activities. People have asked me for copies of the course notes, and different versions of them have been circulating for a few years. Finally I decided that I should really take the time to write the material up in a coherent way and make a book out of it. Here, now, is the result of this work. Over the years many students have been helpful in improving the quality of the notes, and also several colleagues at Linz and elsewhere have contributed to it. I want to thank them all for their effort, in particular I want to thank B. Buchberger, who taught me the theory of Grabner bases nearly two decades ago, B. F. Caviness and B. D. Saunders, who first stimulated my interest in various problems in computer algebra, G. E. Collins, who showed me how to compute in algebraic domains, and J. R. Sendra, with whom I started to apply computer algebra methods to problems in algebraic geometry. Several colleagues have suggested improvements in earlier versions of this book. However, I want to make it clear that I am responsible for all remaining mistakes.

Logic And Computation

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Author : Wilfried Sieg
language : en
Publisher: American Mathematical Soc.
Release Date : 1990

Logic And Computation written by Wilfried Sieg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

This volume contains the proceedings of the Workshop on Logic and Computation, held in July 1987 at Carnegie-Mellon University. The focus of the workshop was the refined interaction between mathematics and computation theory, one of the most fascinating and potentially fruitful developments in logic. The importance of this interaction lies not only in the emergence of the computer as a powerful tool in mathematics research, but also in the various attempts to carry out significant parts of mathematics in computationally informative ways. The proceedings pursue three complementary aims: to develop parts of mathematics under minimal set-theoretic assumptions; to provide formal frameworks suitable for computer implementation; and to extract, from formal proofs, mathematical and computational information. Aimed at logicians, mathematicians, and computer scientists, this volume is rich in results and replete with mathematical, logical, and computational problems.

Parallel Symbolic Computation Pasco 94 Proceedings Of The First International Symposium

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Author : Hoon Hong
language : en
Publisher: World Scientific
Release Date : 1994-09-17

Parallel Symbolic Computation Pasco 94 Proceedings Of The First International Symposium written by Hoon Hong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-09-17 with categories.

These proceedings are devoted to communicating significant developments in all areas pertinent to Parallel Symbolic Computation.The scope includes algorithms, languages, software systems and application in any area of parallel symbolic computation, where parallelism is interpreted broadly to include concurrent, distributive, cooperative schemes, and so forth.

Computing Methods In Applied Sciences And Engineering

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Author : R. Glowinski
language : en
Publisher: SIAM
Release Date : 1990-01-01

Computing Methods In Applied Sciences And Engineering written by R. Glowinski and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Science categories.

"Proceedings of the Ninth International Conference on Computing Methods in Applied Sciences and Engineering, Paris, France, January 29-February 2, 1990"--T.p. verso.

Geospatial Algebraic Computations

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Author : Joseph Awange
language : en
Publisher: Springer
Release Date : 2016-01-29

Geospatial Algebraic Computations written by Joseph Awange and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-29 with Science categories.

Improved geospatial instrumentation and technology such as in laser scanning has now resulted in millions of data being collected, e.g., point clouds. It is in realization that such huge amount of data requires efficient and robust mathematical solutions that this third edition of the book extends the second edition by introducing three new chapters: Robust parameter estimation, Multiobjective optimization and Symbolic regression. Furthermore, the linear homotopy chapter is expanded to include nonlinear homotopy. These disciplines are discussed first in the theoretical part of the book before illustrating their geospatial applications in the applications chapters where numerous numerical examples are presented. The renewed electronic supplement contains these new theoretical and practical topics, with the corresponding Mathematica statements and functions supporting their computations introduced and applied. This third edition is renamed in light of these technological advancements.

Art Of Computer Programming Volume 2

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Author : Donald E. Knuth
language : en
Publisher: Addison-Wesley Professional
Release Date : 2014-05-06

Art Of Computer Programming Volume 2 written by Donald E. Knuth and has been published by Addison-Wesley Professional this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-06 with Computers categories.

The bible of all fundamental algorithms and the work that taught many of today's software developers most of what they know about computer programming. –Byte, September 1995 I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up. –Charles Long If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole thing. –Bill Gates It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers. –Jonathan Laventhol The second volume offers a complete introduction to the field of seminumerical algorithms, with separate chapters on random numbers and arithmetic. The book summarizes the major paradigms and basic theory of such algorithms, thereby providing a comprehensive interface between computer programming and numerical analysis. Particularly noteworthy in this third edition is Knuth's new treatment of random number generators, and his discussion of calculations with formal power series. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP),http://msp.org