Systems of polynomial equations play an important role in many scientific applications. But it is often rather complex and time-consuming to find all -real and complex- solutions. This book describes an efficient algorithm, which uses eigenvalues to compute all solutions of a given system of polynomial equations. For this, the theory of Gröbner bases is combined with numerical linear algebra. Also, a comparison to the performance of existing algorithms is given. Furthermore, a new algorithm to compute the primary decomposition of a zero-dimensional ideal and an algorithm to compute the number of real respectively complex roots of a system of polynomial equations using the quadratic form is delineated. All described algorithms are implemented in the computer algebra system SINGULAR.
Buch Details: |
|
ISBN-13: |
978-3-639-38755-1 |
ISBN-10: |
3639387554 |
EAN: |
9783639387551 |
Buchsprache: |
English |
By (author) : |
Normen Tobias Erbert |
Seitenanzahl: |
144 |
Veröffentlicht am: |
25.01.2012 |
Kategorie: |
Mathematics |