Solving Polynominal Systems Using Continuation for Engineering and Scientific Problems
Published on 4. June 2009
Book
Paperback/Softback
228 pages
978-0-89871-678-8 (ISBN)
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Description
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.
More details
Person
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.
Content
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.
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.