COMPUTING ISOLATED SINGULAR SOLUTIONS OF POLYNOMIAL SYSTEMS: CASE OF BREADTH ONE
We present a symbolic-numeric method to refine an approximate isolated singular solution [Symbol] = ([Symbol]₁,... ,[Symbol] n ) of a polynomial system F = {f₁, ..., f n }, when the Jacobian matrix of F evaluated at × has corank one approximately. Our new approach is based on the regularized Newton...
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| Veröffentlicht in: | SIAM journal on numerical analysis 2012-01, Vol.50 (1), p.354-372 |
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| creator | Li, NAN ZHI, LIHONG |
| description | We present a symbolic-numeric method to refine an approximate isolated singular solution [Symbol] = ([Symbol]₁,... ,[Symbol] n ) of a polynomial system F = {f₁, ..., f n }, when the Jacobian matrix of F evaluated at × has corank one approximately. Our new approach is based on the regularized Newton iteration and the computation of differential conditions satisfied at the approximate singular solution. The size of matrices involved in our algorithm is bounded by n×n. The algorithm converges quadratically if [Symbol] is close to the isolated exact singular solution. |
| doi_str_mv | 10.1137/110827247 |
| format | Article |
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| ispartof | SIAM journal on numerical analysis, 2012-01, Vol.50 (1), p.354-372 |
| issn | 0036-1429 1095-7170 |
| language | eng |
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| source | SIAM Journals Online; Jstor Complete Legacy; JSTOR Mathematics & Statistics |
| subjects | Algebra Algorithms Approximation Differential operators Jacobians Mathematical vectors Matrices Newtons method Polynomials Zero vectors |
| title | COMPUTING ISOLATED SINGULAR SOLUTIONS OF POLYNOMIAL SYSTEMS: CASE OF BREADTH ONE |
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