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Numerical stability of path tracing in polyhedral homotopy continuation methods

Title
Numerical stability of path tracing in polyhedral homotopy continuation methods
Authors
Kim S.Kojima M.
Ewha Authors
김선영
SCOPUS Author ID
김선영scopus
Issue Date
2004
Journal Title
Computing (Vienna/New York)
ISSN
0010-485XJCR Link
Citation
Computing (Vienna/New York) vol. 73, no. 4, pp. 329 - 348
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
The reliability of polyhedral homotopy continuation methods for solving a polynomial system becomes increasingly important as the dimension of the polynomial system increases. High powers of the homotopy continuation parameter t and ill-conditioned Jacobian matrices encountered in tracing of homotopy paths affect the numerical stability. We present modified homotopy functions with a new homotopy continuation parameter s and various scaling strategies to enhance the numerical stability. Advantages of employing the new homotopy parameter 5 are discussed. Numerical results are included to illustrate the improved performance of the presented techniques.
DOI
10.1007/s00607-004-0070-6
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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