Solving Polynominal Systems Using Continuation for Engineering and Scientific Problems

Solving Polynominal Systems Using Continuation for Engineering and Scientific Problems

by Alexander Morgan

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Overview

Polynomial continuation is a numerical technique used to compute solutions to systems of polynomial equations. Originally published in 1987, this introduction to polynomial continuation 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 undergraduate mathematics projects.

Product Details

ISBN-13: 9780898716788
Publisher: SIAM
Publication date: 06/04/2009
Series: Classics in Applied Mathematics Series
Pages: 228
Product dimensions: 6.85(w) x 9.72(h) x 0.67(d)

About the Author

Alexander Morgan retired in 2008 after 30 years as an industrial mathematician with the General Motors Corporation. His research interests include the numerical solution of systems of polynomial equations; the development of practical knowledge systems; and, more recently, data mining, text analysis, and information extraction for healthcare, quality, and warranty databases.

Table of Contents

Preface to the classics edition; Preface; Introduction; Part I. The Method: 1. One equation in one unknown; 2. Two equations in two unknowns; 3. General systems; 4. Implementation; 5. Scaling; 6. Other continuation methods; Part II. Applying the Method: 7. Reduction; 8. Geometric intersection problems; 9. Chemical equilibrium systems; 10. Kinematics of mechanisms; Appendices: Appendix 1. Newton's method; Appendix 2. Emulating complex operations in real arithmetic; Appendix 3. Some real-complex calculus formulas; Appendix 4. Proofs of results from Chapter 3; Appendix 5. Gaussian elimination for system reduction; Appendix 6. Computer programs; Bibliographies and References: Brief bibliography; Addition bibliography; References; Index.

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