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Solving Polynomial Systems Using Continuation for Engineering and Scientific ProblemsSolving Polynomial Systems Using Continuation for Engineering and Scientific Problems

Alexander Morgan



Classics in Applied Mathematics 57

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
This book is accessible to readers with limited mathematical backgrounds who would like to understand how to solve systems of polynomial equations. It is appropriate for undergraduate mechanical engineering courses in which robotics and mechanisms applications are studied.

Contents
Preface to the Classics Edition;
Preface;
Introduction;
Part I: The Method;
Chapter 1: One Equation in One Unknown;
Chapter 2: Two Equations in Two Unknowns;
Chapter 3: General Systems;
Chapter 4: Implementation;
Chapter 5: Scaling;
Chapter 6: Other Continuation Methods;
Part II: Applying the Method;
Chapter 7: Reduction;
Chapter 8: Geometric Intersection Problems;
Chapter 9: Chemical Equilibrium Systems;
Chapter 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

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.

Keywords
polynomial, homotopy, continuation, solving, algebra

2009 / xxiv + 316 pages / Softcover
ISBN: 978-0-898716-78-8
List Price $88.00/ SIAM Member Price $61.60/ Order Code CL57
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