Numerical Algorithms in Algebraic Geometry - Tapa blanda

Al Rashed Shwki

 
9783838113500: Numerical Algorithms in Algebraic Geometry
Tapa blanda
ISBN 10: 3838113500 ISBN 13: 9783838113500
Editorial: Südwestdeutscher Verlag für Hochschulschriften, 2011

Sinopsis

Polynomial systems arise in many applications:robotics, kinematics, chemical kinetics, computer vision, truss design, geometric modeling, and many others. Many polynomial systems have solutions sets, called algebraic varieties, having several irreducible components. A fundamental problem of the numerical algebraic geometry is to decompose such an algebraic variety into its irreducible components. The witness point sets are the natural numerical data structure to encode irreducible algebraic varieties. Sommese, Verschelde and Wampler represented the irreducible algebraic decomposition of an algebraic variety as a union of finite disjoint sets called numerical irreducible decomposition. The sets present the irreducible components. The numerical irreducible decomposition is implemented in Bertini . We modify this concept using partially Groebner bases, triangular sets, local dimension, and the so-called zero sum relation. We present in the second chapter the corresponding algorithms and their implementations in SINGULAR. We give some examples and timings, which show that the modified algorithms are more efficient if the number of variables is not too large.

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Acerca del autor

2004 Bachelor of Science in Mathematics at the University of Damascus, Syria.2005-2007 Study of Mathematics at the University of Kaiserslautern, Germany.2007 Master of Science in Mathematics at the University of Kaiserslautern, Germany.2011 Doctor rerum naturalium, Dr. rer. nat. University of Kaiserslautern.

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Editorial
Südwestdeutscher Verlag für Hochschulschriften
Año de publicación
2011
Idioma
Inglés
ISBN 10 
3838113500
ISBN 13 
9783838113500
Encuadernación
Tapa blanda
Número de páginas
152
Contacto del fabricante
no disponible
Persona responsable
no disponible