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.
Author(s): Alexander Morgan
Series: Classics in Applied Mathematics 57
Year: 2009
Language: English
Pages: 228
Front matter......Page 1
Title page......Page 5
Copyright......Page 6
Contents......Page 9
Preface to the Classics Edition......Page 13
Preface......Page 19
Introduction: Beyond Newton's Method......Page 23
Part I The Method......Page 25
1-1 A Simple Continuation for Solving Quadratic Equations......Page 27
1-2 Singular Paths and the Independence Principle......Page 32
1-3 Solving Higher-Degree Equations......Page 36
1-4 The Geometry of Continuation......Page 38
2-2 Second Degree Equations......Page 43
2-3 Continuation Equations......Page 49
2-4 Solutions at Infinity......Page 51
2-5 Schematics......Page 55
2-6 CONSOL Experiments......Page 56
2-7 Higher-Degree Equations......Page 58
3-2 General Systems......Page 64
3-3 Solutions at Infinity......Page 69
3-4 Continuation......Page 84
4-1 Introduction......Page 96
4-2 CONSOL-E and CONSOL-A......Page 98
4-3 Environmental Issues......Page 103
4-4 Preprocessing......Page 105
4-5 Path Tracking......Page 106
4-6 Performance Evaluation......Page 122
4-7 The Experimental Laboratory......Page 124
5-1 Introduction......Page 131
5-2 Two Scaling Algorithms: SCLGEN and SCLCEN......Page 134
5-3 Computing with SCLGEN and SCLCEN; The Coefficient Tableau......Page 139
6-1 Introduction......Page 144
6-2 General Principles......Page 145
6-3 The Convex-Linear Continuation......Page 159
Part II Applying the Method......Page 169
7-1 Introduction......Page 171
7-2 Reducibility......Page 173
7-3 The Singularity of the SCLGEN Matrix......Page 176
7-4 Row Reducing the Coefficient Matrix......Page 180
8-1 Introduction......Page 183
8-2 Intersection of Two Curves......Page 186
8-3 Intersection of Three Surfaces......Page 198
8-4 Tubes in Space......Page 211
9-1 Introduction......Page 221
9-2 Simple Illustrative Problem......Page 222
9-3 The Methodology in General......Page 227
9-4 Two Combustion Chemistry Examples......Page 229
9-5 A Final Example......Page 240
10-1 Introduction......Page 252
10-2 Revolute Joint Planar Manipulators......Page 253
10-3 Reduction Basics for the Revolute Joint Planar Manipulator......Page 263
10-4 Revolute Joint Spatial Manipulators......Page 271
Appendices......Page 289
Appendix 1 Newton's Method......Page 291
Appendix 2 Emulating Complex Operations in Real Arithmetic......Page 306
Appendix 3 Some Real-Complex Calculus Formulas......Page 308
Appendix 4 Proofs of Results from Chapter 3......Page 315
Appendix 5 Gaussian Elimination for System Reduction......Page 325
Appendix 6 Computer Programs......Page 328
FORTRAN listings - Table of Contents......Page 330
Part A: Complete FORTRAN Programs with complex declarations......Page 332
Part B: Programs without complex declarations......Page 474
Bibliography......Page 559
References......Page 560
Index......Page 565
