Solving Via Eigenvalues: A SINGULAR Implementation - Normen Tobias Erbert
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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 compar ... Full description
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Description
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.
More Information
| Author | Normen Tobias Erbert |
|---|---|
| Publisher | AV Akademikerverlag |
| Release year | 2012 |
| Cover type | Softcover |
| EAN | 9783639387551 |