Algorithms in Real Algebraic GeometrySpringer Science & Business Media, 21. apr. 2007 - 662 sider The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this textbook the main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This second edition contains several recent results, on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number. |
Fra bogen
Resultater 1-5 af 30
... Cauchy Index . . . . . . . . 52 2.3 Projection Theorem for Algebraic Sets . . . . . . . . . . . . . . 57 2.4 Projection Theorem for Semi-Algebraic Sets . . . . . . . . . . 63 2.5 Applications ...
... Cauchy Index . . . . . . 113 Su Co Co 4.3 Quadratic Forms and Root Counting . . . . . . . . . . . . . . . 4.3.1 Quadratic Forms . . . . . . . . . . . . . . . . . . . . . . . 119 4.3.2 Hermite's Quadratic Form ...
... . . 316 8.3.6 Subresultant Computation . . . . . . . . . . . . . . . . . 317 8.4 Bibliographical Notes . . . . . . . . . . . . . . . . . . . . . . . . . 322 10 11 12 9 Cauchy Index and Applications . . Table of Contents VII.
... Cauchy Index and Applications . . . . . . . . . . . . . . . . . . . 323 9.1 Cauchy Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 9.1.1 Computing the Cauchy Index . . . . . . . . . . . . . . . 323 9.1.2 Bezoutian and ...
... to determine whether P has a root in R but also to determine whether P has a root at which another polynomial Q is positive. With this goal in mind, it is profitable to look 52 2 Real Closed Fields Sturm's Theorem and the Cauchy Index.
Indhold
1 | |
11 | |
29 | |
SemiAlgebraic Sets | 83 |
4 | 100 |
Decomposition of SemiAlgebraic Sets | 159 |
6 | 195 |
Quantitative Semialgebraic Geometry | 237 |
Interval | 330 |
Existential Theory of the Reals | 505 |
Quantifier Elimination | 533 |
Computing Roadmaps and Connected Components of Alge | 563 |
Computing Roadmaps and Connected Components of Semi | 593 |
References | 635 |
132 | 641 |
Index of Notation 645 | 644 |
Andre udgaver - Se alle
Algorithms in Real Algebraic Geometry Saugata Basu,Richard Pollack,Marie-Françoise Roy Begrænset visning - 2003 |
Algorithms in Real Algebraic Geometry Saugata Basu,Richard Pollack,Marie-Françoise Roy Begrænset visning - 2006 |
Algorithms in Real Algebraic Geometry Saugata Basu,Richard Pollack,Marie-Françoise Coste-Roy Begrænset visning - 2013 |