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 44
... Betti Numbers of Real Algebraic Sets . . . . . . . 256 7.3 Bounding the Betti Numbers of Realizations of Sign Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 7.4 Sum of the Betti Numbers of ...
... Values and Connectedness . . . . . . . . . . . . 564 15.2 Roadmap of an ... Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 16.2 Uniform ... Betti Number of Semi-algebraic Sets . 627 16.7 Bibliographical Notes ...
... Betti numbers, are an important measure of the topological complexity of semi-algebraic sets, the first of them being the number of connected components of the set. We also define the Euler-Poincaré characteristic, which is a ...
... number of variables. Using the pseudo-critical points introduced in Chapter ... number of variables but rather in the number of blocks of variables appearing in the ... Betti number of semi-algebraic sets. Moreover, it gives an efficient ...
... Betti numbers of semi-algebraic sets in Chapter 7, an improved complexity analysis of real root isolation, as well ... Betti number of a semi-algebraic set in single exponential time. We also included a table of notation and completed ...
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 |