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Effective Polynomial Computation
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Book Synopsis Effective Polynomial Computation by : Richard Zippel
Download or read book Effective Polynomial Computation written by Richard Zippel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Polynomial and Matrix Computations by : Dario Bini
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.
Book Synopsis Polynomial Algorithms in Computer Algebra by : Franz Winkler
Download or read book Polynomial Algorithms in Computer Algebra written by Franz Winkler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Solving Polynomial Equations by : Alicia Dickenstein
Download or read book Solving Polynomial Equations written by Alicia Dickenstein and published by Springer Science & Business Media. This book was released on 2005-04-27 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
Book Synopsis Randomization, Relaxation, and Complexity in Polynomial Equation Solving by : Leonid Gurvits
Download or read book Randomization, Relaxation, and Complexity in Polynomial Equation Solving written by Leonid Gurvits and published by American Mathematical Soc.. This book was released on 2011 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume corresponds to the Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, held from February 28-March 5, 2010. It contains a sample of advanced algorithmic techniques underpinning the solution of systems of polynomial equations. The papers are written by leading experts in algorithmic algebraic geometry and examine core topics.
Book Synopsis Artificial Intelligence and Symbolic Computation by : Jacques Fleuriot
Download or read book Artificial Intelligence and Symbolic Computation written by Jacques Fleuriot and published by Springer. This book was released on 2018-08-27 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Artificial Intelligence and Symbolic Computation, AISC 2018, held in Suzhou, China, in September 2018. The 13 full papers presented together with 5 short and 2 invited papers were carefully reviewed and selected from 31 submissions. The AISC conference is an important forum when it comes to ensuring that ideas, theoretical insights, methods and results from traditional AI can be discussed and showcased, while fostering new links with other areas of AI such as probabilistic reasoning and deep learning.
Book Synopsis Solving Polynomial Equations by : Alicia Dickenstein
Download or read book Solving Polynomial Equations written by Alicia Dickenstein and published by Springer Science & Business Media. This book was released on 2005-12-29 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.
Book Synopsis Artificial Intelligence and Symbolic Computation by : Jaques Calmet
Download or read book Artificial Intelligence and Symbolic Computation written by Jaques Calmet and published by Springer Science & Business Media. This book was released on 2006-09-13 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Conference on Artificial Intelligence and Symbolic Computation, AISC 2006, held in Beijing, China in September 2006. The 18 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 39 submissions. Based on heuristics and mathematical algorithmics, artificial intelligence and symbolic computation are two views and approaches for automating (mathematical) problem solving. The papers address all current aspects in the area of symbolic computing and AI: mathematical foundations, implementations, and applications in industry and academia. The papers are organized in topical sections on artificial intelligence and theorem proving, symbolic computation, constraint satisfaction/solving, and mathematical knowledge management.
Book Synopsis Algorithms and Theory of Computation Handbook - 2 Volume Set by : Mikhail J. Atallah
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
Book Synopsis Error-Free Polynomial Matrix Computations by : E.V. Krishnamurthy
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.
Book Synopsis A Gentle Introduction to Effective Computing in Quantitative Research by : Harry J. Paarsch
Download or read book A Gentle Introduction to Effective Computing in Quantitative Research written by Harry J. Paarsch and published by MIT Press. This book was released on 2016-05-13 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical guide to using modern software effectively in quantitative research in the social and natural sciences. This book offers a practical guide to the computational methods at the heart of most modern quantitative research. It will be essential reading for research assistants needing hands-on experience; students entering PhD programs in business, economics, and other social or natural sciences; and those seeking quantitative jobs in industry. No background in computer science is assumed; a learner need only have a computer with access to the Internet. Using the example as its principal pedagogical device, the book offers tried-and-true prototypes that illustrate many important computational tasks required in quantitative research. The best way to use the book is to read it at the computer keyboard and learn by doing. The book begins by introducing basic skills: how to use the operating system, how to organize data, and how to complete simple programming tasks. For its demonstrations, the book uses a UNIX-based operating system and a set of free software tools: the scripting language Python for programming tasks; the database management system SQLite; and the freely available R for statistical computing and graphics. The book goes on to describe particular tasks: analyzing data, implementing commonly used numerical and simulation methods, and creating extensions to Python to reduce cycle time. Finally, the book describes the use of LaTeX, a document markup language and preparation system.
Book Synopsis Structured Matrices and Polynomials by : Victor Y. Pan
Download or read book Structured Matrices and Polynomials written by Victor Y. Pan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Elimination Methods written by D. Wang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "elimination theory" chapter from from B. his classic Modern Algebra in later editions, A. Weil's hope to eliminate "from algebraic geometry the last traces of elimination theory," and S. Abhyankar's sug gestion to "eliminate the eliminators of elimination theory. " The renaissance and recognition of polynomial elimination owe much to the advent and advance of mod ern computing technology, based on which effective algorithms are implemented and applied to diverse problems in science and engineering. In the last decade, both theorists and practitioners have more and more realized the significance and power of elimination methods and their underlying theories. Active and extensive research has contributed a great deal of new developments on algorithms and soft ware tools to the subject, that have been widely acknowledged. Their applications have taken place from pure and applied mathematics to geometric modeling and robotics, and to artificial neural networks. This book provides a systematic and uniform treatment of elimination algo rithms that compute various zero decompositions for systems of multivariate poly nomials. The central concepts are triangular sets and systems of different kinds, in terms of which the decompositions are represented. The prerequisites for the concepts and algorithms are results from basic algebra and some knowledge of algorithmic mathematics.
Book Synopsis Iterative Methods for Simultaneous Inclusion of Polynomial Zeros by : Miodrag Petkovic
Download or read book Iterative Methods for Simultaneous Inclusion of Polynomial Zeros written by Miodrag Petkovic and published by Lecture Notes in Mathematics. This book was released on 1989-08-09 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The simultaneous inclusion of polynomial complex zeros is a crucial problem in numerical analysis. Rapidly converging algorithms are presented in these notes, including convergence analysis in terms of circular regions, and in complex arithmetic. Parallel circular iterations, where the approximations to the zeros have the form of circular regions containing these zeros, are efficient because they also provide error estimates. There are at present no book publications on this topic and one of the aims of this book is to collect most of the algorithms produced in the last 15 years. To decrease the high computational cost of interval methods, several effective iterative processes for the simultaneous inclusion of polynomial zeros which combine the efficiency of ordinary floating-point arithmetic with the accuracy control that may be obtained by the interval methods, are set down, and their computational efficiency is described. The rate of these methods is of interest in designing a package for the simultaneous approximation of polynomial zeros, where automatic procedure selection is desired. The book is both a text and a reference source for mathematicans, engineers, physicists and computer scientists who are interested in new developments and applications, but the material is also accessible to anyone with graduate level mathematical background and some knowledge of basic computational complex analysis and programming.
Book Synopsis The Nature of Computation by : Cristopher Moore
Download or read book The Nature of Computation written by Cristopher Moore and published by Oxford University Press. This book was released on 2011-08-11 with total page 1004 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Modern Computer Algebra by : Joachim von zur Gathen
Download or read book Modern Computer Algebra written by Joachim von zur Gathen and published by Cambridge University Press. This book was released on 2013-04-25 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.
Book Synopsis Computer Algebra in Scientific Computing by : François Boulier
Download or read book Computer Algebra in Scientific Computing written by François Boulier and published by Springer Nature. This book was released on 2023-08-23 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 25th International Workshop on Computer Algebra in Scientific Computing, CASC 2023, which took place in Havana, Cuba, during August 28-September 1, 2023. The 22 full papers included in this book were carefully reviewed and selected from 29 submissions. They focus on the theory of symbolic computation and its implementation in computer algebra systems as well as all other areas of scientific computing with regard to their benefit from or use of computer algebra methods and software.
