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On the Differential and Full Algebraic Complexities of Operator Matrices Transformations Read chapter Read first chapter

2016 | OriginalPaper | Chapter

A Numerical Method for Computing Border Curves of Bi-parametric Real Polynomial Systems and Applications

Authors : Changbo Chen, Wenyuan Wu

Published in: Computer Algebra in Scientific Computing

Publisher: Springer International Publishing

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Abstract

For a bi-parametric real polynomial system with parameter values restricted to a finite rectangular region, under certain assumptions, we introduce the notion of border curve. We propose a numerical method to compute the border curve, and provide a numerical error estimation.
The border curve enables us to construct a so-called “solution map”. For a given value u of the parameters inside the rectangle but not on the border, the solution map tells the subset that u belongs to together with a connected path from the corresponding sample point w to u. Consequently, all the real solutions of the system at u (which are isolated) can be obtained by tracking a real homotopy starting from all the real roots at w throughout the path. The effectiveness of the proposed method is illustrated by some examples.

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previous chapter Incompleteness, Undecidability and Automated Proofs
next chapter The Complexity of Cylindrical Algebraic Decomposition with Respect to Polynomial Degree
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Metadata
Title
A Numerical Method for Computing Border Curves of Bi-parametric Real Polynomial Systems and Applications
Authors
Changbo Chen
Wenyuan Wu
Copyright Year
2016
Book
Computer Algebra in Scientific Computing

Print ISBN: 978-3-319-45640-9

Electronic ISBN: 978-3-319-45641-6

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-45641-6_11

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