The numerical solution of systems of polynomials arising in engineering and science:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ
World Scientific
2005
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (pages 379-395) and index 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 |
| Beschreibung: | 1 Online-Ressource (xxii, 401 pages) |
| ISBN: | 1281880825 9781281880826 9789812561848 9789812567727 9812561846 9812567720 |
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| 245 | 1 | 0 | |a The numerical solution of systems of polynomials arising in engineering and science |c by Andrew J. Sommese and Charles W. Wampler, II. |
| 264 | 1 | |a Hackensack, NJ |b World Scientific |c 2005 | |
| 300 | |a 1 Online-Ressource (xxii, 401 pages) | ||
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| 500 | |a Includes bibliographical references (pages 379-395) and index | ||
| 500 | |a 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 -- | ||
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| 500 | |a - 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 -- | ||
| 500 | |a - 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 | ||
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Datensatz im Suchindex
| _version_ | 1804175528764112896 |
|---|---|
| any_adam_object | |
| author | Sommese, Andrew John |
| author_facet | Sommese, Andrew John |
| author_role | aut |
| author_sort | Sommese, Andrew John |
| author_variant | a j s aj ajs |
| building | Verbundindex |
| bvnumber | BV043110054 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)63201945 (DE-599)BVBBV043110054 |
| dewey-full | 512/.9422 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.9422 |
| dewey-search | 512/.9422 |
| dewey-sort | 3512 49422 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:44Z |
| institution | BVB |
| isbn | 1281880825 9781281880826 9789812561848 9789812567727 9812561846 9812567720 |
| language | English |
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| publisher | World Scientific |
| record_format | marc |
| spelling | Sommese, Andrew John Verfasser aut The numerical solution of systems of polynomials arising in engineering and science by Andrew J. Sommese and Charles W. Wampler, II. Hackensack, NJ World Scientific 2005 1 Online-Ressource (xxii, 401 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (pages 379-395) and index 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 Polynômes MATHEMATICS / Algebra / Elementary bisacsh Polynomials Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Polynom (DE-588)4046711-9 s 1\p DE-604 Numerisches Verfahren (DE-588)4128130-5 s 2\p DE-604 Algebraische Geometrie (DE-588)4001161-6 s 3\p DE-604 Wampler, Charles Weldon Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=148565 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sommese, Andrew John The numerical solution of systems of polynomials arising in engineering and science Polynômes MATHEMATICS / Algebra / Elementary bisacsh Polynomials Numerisches Verfahren (DE-588)4128130-5 gnd Polynom (DE-588)4046711-9 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4046711-9 (DE-588)4001161-6 |
| title | The numerical solution of systems of polynomials arising in engineering and science |
| title_auth | The numerical solution of systems of polynomials arising in engineering and science |
| title_exact_search | The numerical solution of systems of polynomials arising in engineering and science |
| title_full | The numerical solution of systems of polynomials arising in engineering and science by Andrew J. Sommese and Charles W. Wampler, II. |
| title_fullStr | The numerical solution of systems of polynomials arising in engineering and science by Andrew J. Sommese and Charles W. Wampler, II. |
| title_full_unstemmed | The numerical solution of systems of polynomials arising in engineering and science by Andrew J. Sommese and Charles W. Wampler, II. |
| title_short | The numerical solution of systems of polynomials arising in engineering and science |
| title_sort | the numerical solution of systems of polynomials arising in engineering and science |
| topic | Polynômes MATHEMATICS / Algebra / Elementary bisacsh Polynomials Numerisches Verfahren (DE-588)4128130-5 gnd Polynom (DE-588)4046711-9 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Polynômes MATHEMATICS / Algebra / Elementary Polynomials Numerisches Verfahren Polynom Algebraische Geometrie |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=148565 |
| work_keys_str_mv | AT sommeseandrewjohn thenumericalsolutionofsystemsofpolynomialsarisinginengineeringandscience AT wamplercharlesweldon thenumericalsolutionofsystemsofpolynomialsarisinginengineeringandscience |