Last edited by Vulrajas
Wednesday, August 5, 2020 | History

7 edition of Numerical Polynomial Algebra found in the catalog.

Numerical Polynomial Algebra

by Hans J. Stetter

  • 374 Want to read
  • 16 Currently reading

Published by SIAM: Society for Industrial and Applied Mathematics .
Written in English

    Subjects:
  • Algebra,
  • Numerical analysis,
  • Mathematics,
  • Science/Mathematics,
  • Algebra - Elementary,
  • Mathematics / Algebra / General,
  • General,
  • Polynomials

  • The Physical Object
    FormatPaperback
    Number of Pages488
    ID Numbers
    Open LibraryOL8271943M
    ISBN 100898715571
    ISBN 109780898715576

      Numerical polynomial algebra emerges as a growing field of study in recent years with a broad spectrum of applications and many robust algorithms. Among the challenges we must face when solving polynomial algebra problems with floating-point arithmetic, the most frequently encountered difficulties include the regularization of ill-posedness and Cited by: 8. The book covers less mathematics than a typical text on applied linear algebra. We use only one theoretical concept from linear algebra, linear independence, and only one computational tool, the QR factorization; our approach to most applica-tions relies on only one method, least squares (or some extension). In this sense.

    The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively.5/5(1). Algebra The word \algebra" means many things. The word dates back about years ago to part of the title of al-Khwarizm ’s book on the subject, but the subject itself goes back years ago to ancient Babylonia and Egypt. It was about solving numerical problems that we would now identify as linear and quadratic Size: 1MB.

    The set of solutions to a system of polynomial equations is an algebraic variety, the basic object of algebraic geometry. The algorithmic study of algebraic vari-eties is the central theme of computational algebraic geometry. Exciting recent developments in symbolic algebra and numerical software for geometric calcu-. List of Figures Fig. NLALIB hierarchy. xxv Fig. Matrix multiplication. 3 Fig. Rotating the xy-plane. 7 Fig. Rotated line 8 Fig. Rotate three-dimensional coordinate - Selection from Numerical Linear Algebra with Applications [Book].


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Numerical Polynomial Algebra by Hans J. Stetter Download PDF EPUB FB2

This book is the first comprehensive treatment of numerical polynomial algebra, an emerging area that falls between classical numerical analysis and classical computer algebra, and which has received surprisingly little attention so far.

The author introduces a conceptual framework that permits the meaningful solution of various algebraic Cited by: This book offers an interesting approach, combining numerical analysis and polynomial algebra.

The emphasis is on multivariate polynomial systems arising in problems from scientific computing, and their solution with methods adopted from numerical analysis, instead of methods from computer algebra. 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.

"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." "Graduate students or academic and industrial research scientists in numerical analysis and computer algebra can use Numerical Polynomial Algebra as a.

The high accuracy required by facial reduction and also the ill-conditioning commonly encountered in numerical polynomial algebra [23] motivated us Numerical Polynomial Algebra book implement Douglas-Rachford iteration in [ In mathematics, an integer-valued polynomial (also known as a numerical polynomial) P(t) is a polynomial whose value P(n) is an integer for every integer polynomial with integer coefficients is integer-valued, but the converse is not true.

For example, the polynomial + = (+) takes on integer values whenever t is an integer. That Numerical Polynomial Algebra book because one of t and t + 1 must be an.

Introductory Observations. In Part II of this book, we have seen that the numerical algebra of univariate polynomials is governed by a relatively small number of guiding principles: Algebraically, there is the simple structure of a principal ideal, with one generating polynomial which is unique except for a scalar factor, and of a quotient ring and dual space of the same.

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 5/5(3).

The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world.

'This first book on the numerical analysis of polynomial systems is a stepping stone at the interface of symbolic computation and numerical computation.' Bernard Sturmfels, University of Berkeley 'I am not familiar with any books that do such a careful job of combining numerical analysis with the algebra of polynomial equations.

In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.

Polynomial rings occur in many parts of mathematics, and the study of their properties was. Numerical Polynomial Algebra Combining approaches of both numerical linear algebra and commutative algebra, this clearly-written text provides both a survey of polynomial problems in scientific computing that may be solved numerically and a guide to their numerical treatment.

$\begingroup$ Numerical linear algebra is not the right use case for Maple. Maple is more suitable for symbolic/exact computations e.g.

over $\mathbb{Z}, \mathbb{Q}$, finite fields, and algebraic numbers. MATLAB, however, is (one of) the right tools for computational numerical linear algebra. $\endgroup$ – user Mar 3 '12 at Preface; Part I: Polynomials and Numerical Analysis; Chapter 1: Polynomials; Chapter 2: Representations of Polynomial Ideals; Chapter 3: Polynomials with Coefficients of Limited Accuracy; Chapter 4: Approximate Numerical Computation; Part II: Univariate Polynomial Problems; Chapter 5: Univariate Polynomials; Chapter 6: Various Tasks with Empirical.

Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations.

The book breaks with tradition by beginning not with Gaussian elimination, but with the QR factorization--a more important and fresher idea for students, and the thread that connects most of the algorithms of numerical linear algebra, including methods for least squares, eigenvalue, and singular value problems, as well as iterative methods for.

Numerical analysis explains why numerical computations work, or fail. This book is divided into four parts. Part I starts Part I starts with a guided tour of floating number systems and machine arithmetic. The exponential and the logarithm are constructed from scratch to present a new point ofview on questions well-known to the reader, and the needed knowledge of linear algebra is.

Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear.

A concise, insightful, and elegant introduction to the field of numerical linear algebra. Designed for use as a stand-alone textbook in a one-semester, graduate-level course in the topic, it has already been class-tested by MIT and Cornell graduate students from all fields of mathematics, engineering, and the physical sciences.

The authors' clear, inviting style and evident love. This book is the first comprehensive treatment of Numerical polynomial algebra, an area which so far has received little attention.

英文书摘要 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. Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques.

Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and .College Algebra for STEM. This book is designed specifically as a College Algebra course for prospective STEM students.

Topics covered includes: Review of Beginning/Intermediate Algebra, Functions and Related Topics, Polynomial Functions, Rational Functions, Exponential and Logarithmic Functions. Author(s): Marcel B.

Finan.troduction to abstract linear algebra for undergraduates, possibly even first year students, specializing in mathematics.

Linear algebra is one of the most applicable areas of mathematics. It is used by the pure mathematician and by the mathematically trained scien-tists of all disciplines. This book is directed more at the former audienceFile Size: 1MB.