Numerical Polynomial Algebra

Author : Hans J. Stetter
Publisher : SIAM
Page : 487 pages
File Size : 53,6 Mb
Release : 2004-01-01
Category : Mathematics
ISBN : 0898717973

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Numerical Polynomial Algebra by Hans J. Stetter Pdf

In many important areas of scientific computing, polynomials in one or more variables are employed in the mathematical modeling of real-life phenomena; yet most of classical computer algebra assumes exact rational data. This book is the first comprehensive treatment of the emerging area of numerical polynomial algebra, an area that falls between classical numerical analysis and classical computer algebra but, surprisingly, has received little attention so far. The author introduces a conceptual framework that permits the meaningful solution of various algebraic problems with multivariate polynomial equations whose coefficients have some indeterminacy; for this purpose, he combines approaches of both numerical linear algebra and commutative algebra. For the application scientist, Numerical Polynomial Algebra provides both a survey of polynomial problems in scientific computing that may be solved numerically and a guide to their numerical treatment. In addition, the book provides both introductory sections and novel extensions of numerical analysis and computer algebra, making it accessible to the reader with expertise in either one of these areas.

Author : Daniel J. Bates,Jonathan D. Hauenstein,Andrew J. Sommese,Charles W. Wampler
Publisher : SIAM
Page : 372 pages
File Size : 53,9 Mb
Release : 2013-11-08
Category : Science
ISBN : 9781611972702

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Numerically Solving Polynomial Systems with Bertini by Daniel J. Bates,Jonathan D. Hauenstein,Andrew J. Sommese,Charles W. Wampler Pdf

This book is a guide to concepts and practice in numerical algebraic geometry ? the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.

Author : J.M. McNamee,Victor Pan
Publisher : Newnes
Page : 728 pages
File Size : 46,9 Mb
Release : 2013-07-19
Category : Mathematics
ISBN : 9780080931432

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Numerical Methods for Roots of Polynomials - by J.M. McNamee,Victor Pan Pdf

Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to certain modern virtually optimal methods. Additionally, there are pointers to robust and efficient programs. This book is invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. First comprehensive treatment of Root-Finding in several decades with a description of high-grade software and where it can be downloaded Offers a long chapter on matrix methods and includes Parallel methods and errors where appropriate Proves invaluable for research or graduate course

Author : Andrew J Sommese,Charles W Wampler, Ii
Publisher : World Scientific
Page : 425 pages
File Size : 52,6 Mb
Release : 2005-03-21
Category : Mathematics
ISBN : 9789814480888

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The Numerical Solution Of Systems Of Polynomials Arising In Engineering And Science by Andrew J Sommese,Charles W Wampler, Ii Pdf

Written by the founders of the new and expanding field of numerical algebraic geometry, this is the first book that uses an algebraic-geometric approach to the numerical solution of polynomial systems and also the first one to treat numerical methods for finding positive dimensional solution sets. The text covers the full theory from methods developed for isolated solutions in the 1980's to the most recent research on positive dimensional sets.

Author : Jaime Gutierrez,Josef Schicho,Martin Weimann
Publisher : Springer
Page : 222 pages
File Size : 55,5 Mb
Release : 2015-01-20
Category : Computers
ISBN : 9783319150819

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Computer Algebra and Polynomials by Jaime Gutierrez,Josef Schicho,Martin Weimann Pdf

Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.

Author : Alexander Morgan
Publisher : SIAM
Page : 331 pages
File Size : 49,8 Mb
Release : 2009-01-01
Category : Computers
ISBN : 9780898719031

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Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems by Alexander Morgan Pdf

This book introduces the numerical technique of polynomial continuation, which is used to compute solutions to systems of polynomial equations. Originally published in 1987, it remains a useful starting point for the reader interested in learning how to solve practical problems without advanced mathematics. Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems is easy to understand, requiring only a knowledge of undergraduate-level calculus and simple computer programming. The book is also practical; it includes descriptions of various industrial-strength engineering applications and offers Fortran code for polynomial solvers on an associated Web page. It provides a resource for high-school and undergraduate mathematics projects. Audience: accessible to readers with limited mathematical backgrounds. It is appropriate for undergraduate mechanical engineering courses in which robotics and mechanisms applications are studied.

Author : J. M. McNamee
Publisher : Unknown
Page : 128 pages
File Size : 49,8 Mb
Release : 2007
Category : Equations, Roots of
ISBN : LCCN:2010293020

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Numerical Methods for Roots of Polynomials by J. M. McNamee Pdf

Author : James V Lambers,Amber C Sumner Mooney,Vivian Ashley Montiforte
Publisher : World Scientific
Page : 691 pages
File Size : 53,5 Mb
Release : 2021-01-14
Category : Mathematics
ISBN : 9789811227950

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Explorations In Numerical Analysis: Python Edition by James V Lambers,Amber C Sumner Mooney,Vivian Ashley Montiforte Pdf

This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations.Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language.This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.

Author : Paul A. Fuhrmann
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 46,6 Mb
Release : 2012-10-01
Category : Mathematics
ISBN : 9781441987341

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A Polynomial Approach to Linear Algebra by Paul A. Fuhrmann Pdf

A Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra. Finally there is a chapter on Hankel norm approximation for the case of scalar rational functions which allows the reader to access ideas and results on the frontier of current research.

Author : Dario Bini,Victor Y. Pan
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461202653

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Polynomial and Matrix Computations by Dario Bini,Victor Y. Pan Pdf

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 : E.J. Barbeau
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 45,8 Mb
Release : 2003-10-09
Category : Mathematics
ISBN : 0387406271

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Polynomials by E.J. Barbeau Pdf

The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and congruences. The theory is not treated formally, but rather illustrated through examples. Over 300 problems drawn from journals, contests, and examinations test understanding, ingenuity, and skill. Each chapter ends with a list of hints; there are answers to many of the exercises and solutions to all of the problems. In addition, 69 "explorations" invite the reader to investigate research problems and related topics.

Author : Edward Barbeau
Publisher : New York : Springer-Verlag
Page : 472 pages
File Size : 45,8 Mb
Release : 1989
Category : Mathematics
ISBN : UOM:39015015615324

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Polynomials by Edward Barbeau Pdf

This book provides a backdrop for study in calculus, modern algebra, numerical analysis and complex variable theory, through examples. Includes some 300 problems drawn from journals, contests, and examinations to test understanding, ingenuity, and skill.

Author : Claude Brezinski
Publisher : CRC Press
Page : 181 pages
File Size : 50,6 Mb
Release : 2020-08-11
Category : Mathematics
ISBN : 9781000104738

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Biorthogonality and its Applications to Numerical Analysis by Claude Brezinski Pdf

This book explores the use of the concept of biorthogonality and discusses the various recurrence relations for the generalizations of the method of moments, the method of Lanczos, and the biconjugate gradient method. It is helpful for researchers in numerical analysis and approximation theory.

Author : Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov
Publisher : Springer
Page : 515 pages
File Size : 47,8 Mb
Release : 2014-09-01
Category : Computers
ISBN : 9783319105154

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Computer Algebra in Scientific Computing by Vladimir P. Gerdt,Wolfram Koepf,Werner M. Seiler,Evgenii V. Vorozhtsov Pdf

This book constitutes the proceedings of the 16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014, held in Warsaw, Poland, in September 2014. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as Studies in polynomial algebra are represented by contributions devoted to factoring sparse bivariate polynomials using the priority queue, the construction of irreducible polynomials by using the Newton index, real polynomial root finding by means of matrix and polynomial iterations, application of the eigenvalue method with symmetry for solving polynomial systems arising in the vibration analysis of mechanical structures with symmetry properties, application of Gröbner systems for computing the (absolute) reduction number of polynomial ideals, the application of cylindrical algebraic decomposition for solving the quantifier elimination problems, certification of approximate roots of overdetermined and singular polynomial systems via the recovery of an exact rational univariate representation from approximate numerical data, new parallel algorithms for operations on univariate polynomials (multi-point evaluation, interpolation) based on subproduct tree techniques.

Author : E.V. Krishnamurthy
Publisher : Springer Science & Business Media
Page : 170 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461251187

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Error-Free Polynomial Matrix Computations by E.V. Krishnamurthy Pdf

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.