Author: Alston Scott Householder
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 552
Book Description
KWIC Index for Numerical Algebra
Author: Alston Scott Householder
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 552
Book Description
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 552
Book Description
Algorithms for Computer Algebra
Author: Keith O. Geddes
Publisher: Springer Science & Business Media
ISBN: 0585332479
Category : Computers
Languages : en
Pages : 594
Book Description
Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.
Publisher: Springer Science & Business Media
ISBN: 0585332479
Category : Computers
Languages : en
Pages : 594
Book Description
Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.
Research in Progress
Author:
Publisher:
ISBN:
Category : Military research
Languages : en
Pages : 834
Book Description
Publisher:
ISBN:
Category : Military research
Languages : en
Pages : 834
Book Description
A Survey of Numerical Mathematics
Author: David M. Young
Publisher: Courier Corporation
ISBN: 0486656918
Category : Mathematics
Languages : en
Pages : 562
Book Description
Volume I of two-volume set offers broad self-contained coverage of computer-oriented numerical algorithms for solving mathematical problems related to linear algebra, ordinary and partial differential equations, and much more. 1972 edition.
Publisher: Courier Corporation
ISBN: 0486656918
Category : Mathematics
Languages : en
Pages : 562
Book Description
Volume I of two-volume set offers broad self-contained coverage of computer-oriented numerical algorithms for solving mathematical problems related to linear algebra, ordinary and partial differential equations, and much more. 1972 edition.
Collected Algorithms from ACM
Author: Association for Computing Machinery
Publisher:
ISBN:
Category : ALGOL (Computer program language)
Languages : en
Pages : 716
Book Description
Publisher:
ISBN:
Category : ALGOL (Computer program language)
Languages : en
Pages : 716
Book Description
U.S. Government Research & Development Reports
Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 784
Book Description
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 784
Book Description
Scientific and Technical Aerospace Reports
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages :
Book Description
Collected Algorithms from ACM.
Author:
Publisher:
ISBN:
Category : ALGOL (Computer program language)
Languages : en
Pages : 720
Book Description
Publisher:
ISBN:
Category : ALGOL (Computer program language)
Languages : en
Pages : 720
Book Description
Matrix Algebra
Author: James E. Gentle
Publisher: Springer
ISBN: 3319648675
Category : Mathematics
Languages : en
Pages : 664
Book Description
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
Publisher: Springer
ISBN: 3319648675
Category : Mathematics
Languages : en
Pages : 664
Book Description
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
Methods and Applications of Error-Free Computation
Author: R. T. Gregory
Publisher: Springer Science & Business Media
ISBN: 1461252423
Category : Mathematics
Languages : en
Pages : 204
Book Description
This book is written as an introduction to the theory of error-free computation. In addition, we include several chapters that illustrate how error-free com putation can be applied in practice. The book is intended for seniors and first year graduate students in fields of study involving scientific computation using digital computers, and for researchers (in those same fields) who wish to obtain an introduction to the subject. We are motivated by the fact that there are large classes of ill-conditioned problems, and there are numerically unstable algorithms, and in either or both of these situations we cannot tolerate rounding errors during the numerical computations involved in obtaining solutions to the problems. Thus, it is important to study finite number systems for digital computers which have the property that computation can be performed free of rounding errors. In Chapter I we discuss single-modulus and multiple-modulus residue number systems and arithmetic in these systems, where the operands may be either integers or rational numbers. In Chapter II we discuss finite-segment p-adic number systems and their relationship to the p-adic numbers of Hensel [1908]. Each rational number in a certain finite set is assigned a unique Hensel code and arithmetic operations using Hensel codes as operands is mathe matically equivalent to those same arithmetic operations using the cor responding rational numbers as operands. Finite-segment p-adic arithmetic shares with residue arithmetic the property that it is free of rounding errors.
Publisher: Springer Science & Business Media
ISBN: 1461252423
Category : Mathematics
Languages : en
Pages : 204
Book Description
This book is written as an introduction to the theory of error-free computation. In addition, we include several chapters that illustrate how error-free com putation can be applied in practice. The book is intended for seniors and first year graduate students in fields of study involving scientific computation using digital computers, and for researchers (in those same fields) who wish to obtain an introduction to the subject. We are motivated by the fact that there are large classes of ill-conditioned problems, and there are numerically unstable algorithms, and in either or both of these situations we cannot tolerate rounding errors during the numerical computations involved in obtaining solutions to the problems. Thus, it is important to study finite number systems for digital computers which have the property that computation can be performed free of rounding errors. In Chapter I we discuss single-modulus and multiple-modulus residue number systems and arithmetic in these systems, where the operands may be either integers or rational numbers. In Chapter II we discuss finite-segment p-adic number systems and their relationship to the p-adic numbers of Hensel [1908]. Each rational number in a certain finite set is assigned a unique Hensel code and arithmetic operations using Hensel codes as operands is mathe matically equivalent to those same arithmetic operations using the cor responding rational numbers as operands. Finite-segment p-adic arithmetic shares with residue arithmetic the property that it is free of rounding errors.