The numerical solution of systems of polynomials arising in engineering and science / by Andrew J. Sommese and Charles W. Wampler, II.

Includes bibliographical references (pages 379-395) and index.

Print version record.

Cover -- Preface -- Contents -- Conventions -- PART I Background -- Chapter 1 Polynomial Systems -- 1.1 Polynomials in One Variable -- 1.2 Multivariate Polynomial Systems -- 1.3 Trigonometric Equations as Polynomials -- 1.4 Solution Sets -- 1.5 Solution by Continuation -- 1.6 Overview -- 1.7 Exercises -- Chapter 2 Homotopy Continuation -- 2.1 Continuation for Polynomials in One Variable -- 2.2 Complex Versus Real Solutions -- 2.3 Path Tracking -- 2.4 Exercises -- Chapter 3 Projective Spaces -- 3.1 Motivation: Quadratic Equations -- 3.2 Definition of Projective Space -- 3.3 The Projective Line P1 -- 3.4 The Projective Plane P2 -- 3.5 Projective Algebraic Sets -- 3.6 Multiprojective Space -- 3.7 Tracking Solutions to Infinity -- 3.8 Exercises -- Chapter 4 Genericity and Probability One -- 4.1 Generic Points -- 4.2 Example: Generic Lines -- 4.3 Probabilistic Null Test -- 4.4 Algebraic Probability One -- 4.5 Numerical Certainty -- 4.6 Other Approaches to Genericity -- 4.7 Final Remarks -- 4.8 Exercises -- Chapter 5 Polynomials of One Variable -- 5.1 Some Algebraic Facts about Polynomials of One Complex Variable -- 5.2 Some Analytic Facts about Polynomials of One Complex Variable (Optional) -- 5.3 Some Numerical Aspects of Polynomials of One Variable -- 5.4 Exercises -- Chapter 6 Other Methods -- 6.1 Exclusion Methods -- 6.2 Elimination Methods -- 6.3 Gr246;bner Methods -- 6.4 More Methods -- 6.5 Floating Point vs. Exact Arithmetic -- 6.6 Discussion -- 6.7 Exercises -- PART II Isolated Solutions -- Chapter 7 Coefficient-Parameter Homotopy -- 7.1 Coefficient-Parameter Theory -- 7.2 Parameter Homotopy in Application -- 7.3 An Illustrative Example: Triangles -- 7.4 Nested Parameter Homotopies -- 7.5 Side Conditions -- 7.6 Homotopies that Respect Symmetry Groups -- 7.7 Case Study: Stewart-Gough Platforms -- 7.8 Historical Note: The Cheaters Homotopy -- 7.9 Exercises -- Chapter 8 Polynomial Structures -- 8.1 A Hierarchy of Structures -- 8.2 Notation -- 8.3 Homotopy Paths for Linearly Parameterized Families -- 8.4 Product Homotopies -- 8.5 Polytope Structures -- 8.6 A Summarizing Example -- 8.7 Exercises -- Chapter 9 Case Studies -- 9.1 Nash Equilibria -- 9.2 Chemical Equilibrium -- 9.3 Stewart-Gough Forward Kinematics -- 9.4 Six-Revolute Serial-Link Robots -- 9.5 Planar Seven-Bar Structures -- 9.6 Four-Bar Linkage Design -- 9.7 Exercises -- Chapter 10 Endpoint Estimation -- 10.1 Nonsingular Endpoints -- 10.2 Singular Endpoints -- 10.3 Singular Endgames -- 10.4 Losing the Endgame -- 10.5 Deflation of Isolated Singularities -- 10.6 Exercises -- Chapter 11 Checking Results and Other Implementation Tips -- 11.1 Checks -- 11.2 Corrective Actions -- 11.3 Exercises -- PART III Positive Dimensional Solutions -- Chapter 12 Basic Algebraic Geometry -- 12.1 Affine Algebraic Sets -- 12.2 The Irreducible Decomposition for Affine Algebraic Sets -- 12.3 Further Remarks on Projective Algebraic Sets -- 12.4 Quasiprojective Algebraic Sets -- 12.5 Constructible Algebraic Sets -- 12.6 Multiplicity -- 12.7 Exercises -- Chapter 13 Basic Numerical Algebraic Geometry -- 13.1 Introduction to Witness Sets -- 13.2 Linear Slicing.

English.

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