Effective Polynomial Computation
Effective Polynomial Computation

Author: Richard Zippel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 364

ISBN-13: 1461531888

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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.

Algorithms and Theory of Computation Handbook, Volume 1
Algorithms and Theory of Computation Handbook, Volume 1

Author: Mikhail J. Atallah

Publisher: CRC Press

Published: 2009-11-20

Total Pages: 974

ISBN-13: 1584888237

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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

Algorithms and Theory of Computation Handbook - 2 Volume Set
Algorithms and Theory of Computation Handbook - 2 Volume Set

Author: Mikhail J. Atallah

Publisher: CRC Press

Published: 2022-05-29

Total Pages: 1904

ISBN-13: 1439832331

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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

Mathematical Tools for Physicists
Mathematical Tools for Physicists

Author: Michael Grinfeld

Publisher: John Wiley & Sons

Published: 2014-11-05

Total Pages: 634

ISBN-13: 3527684271

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The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.

Algorithms and Computation
Algorithms and Computation

Author: Toshihide Ibaraki

Publisher: Springer

Published: 2003-11-24

Total Pages: 764

ISBN-13: 3540245871

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This volume contains the proceedings of the 14th Annual International S- posium on Algorithms and Computation (ISAAC 2003), held in Kyoto, Japan, 15–17 December 2003. In the past, it was held in Tokyo (1990), Taipei (1991), Nagoya (1992), Hong Kong (1993), Beijing (1994), Cairns (1995), Osaka (1996), Singapore (1997), Taejon (1998), Chennai (1999), Taipei (2000), Christchurch (2001), and Vancouver (2002). ISAACisanannualinternationalsymposiumthatcoverstheverywiderange of topics in algorithms and computation. The main purpose of the symposium is to provide a forum for researchers working in algorithms and the theory of computation where they can exchange ideas in this active research community. In response to our call for papers, we received unexpectedly many subm- sions, 207 papers. The task of selecting the papers in this volume was done by our program committee and referees. After a thorough review process, the committee selected 73 papers. The selection was done on the basis of originality and relevance to the ?eld of algorithms and computation. We hope all accepted papers will eventally appear in scienti?c journals in more polished forms. The best paper award was given for “On the Geometric Dilation of Finite Point Sets” to Annette Ebbers-Baumann, Ansgar Grune ̈ and Rolf Klein. Two eminent invited speakers, Prof. Andrew Chi-Chih Yao of Princeton University and Prof. Takao Nishizeki of Tohoku University, contributed to this proceedings.

Polynomial and Matrix Computations
Polynomial and Matrix Computations

Author: Dario Bini

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 433

ISBN-13: 1461202655

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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.

The Nature of Computation
The Nature of Computation

Author: Cristopher Moore

Publisher: Oxford University Press

Published: 2011-08-11

Total Pages: 1004

ISBN-13: 0199233217

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The boundary between physics and computer science has become a hotbed of interdisciplinary collaboration. In this book the authors introduce the reader to the fundamental concepts of computational complexity and give in-depth explorations of the major interfaces between computer science and physics.

Well-Quasi Orders in Computation, Logic, Language and Reasoning
Well-Quasi Orders in Computation, Logic, Language and Reasoning

Author: Peter M. Schuster

Publisher: Springer Nature

Published: 2020-01-01

Total Pages: 395

ISBN-13: 3030302296

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This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.

Logic and Computation
Logic and Computation

Author: Wilfried Sieg

Publisher: American Mathematical Soc.

Published: 1990

Total Pages: 314

ISBN-13: 0821851101

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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
Parallel Symbolic Computation Pasco '94 - Proceedings Of The First International Symposium

Author: Hoon Hong

Publisher: World Scientific

Published: 1994-09-17

Total Pages: 450

ISBN-13: 9814550108

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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.