Algorithm 931
Algorithm 931, an algorithm and software for computing multiplicity structures at zeros of nonlinear systems. A MATLAB implementation, multiplicity, of a numerical algorithm for computing the multiplicity structure of a nonlinear system at an isolated zero is presented. The software incorporates a newly developed equation-by-equation strategy that significantly improves the efficiency of the closedness subspace algorithm and substantially reduces the storage requirement. The equation-by-equation strategy is actually based on a variable-by-variable closedness subspace approach. As a result, the algorithm and software can handle much larger nonlinear systems and higher multiplicities than their predecessors, as shown in computational experiments on the included test suite of benchmark problems.
This software is also peer reviewed by journal TOMS.
This software is also peer reviewed by journal TOMS.
Keywords for this software
References in zbMATH (referenced in 9 articles , 1 standard article )
Showing results 1 to 9 of 9.
Sorted by year (- Cheng, Jin-San; Dou, Xiaojie; Wen, Junyi: A new deflation method for verifying the isolated singular zeros of polynomial systems (2020)
- Hao, Wenrui; Hesthaven, Jan; Lin, Guang; Zheng, Bin: A homotopy method with adaptive basis selection for computing multiple solutions of differential equations (2020)
- Batselier, Kim; Wong, Ngai: Inverse multivariate polynomial root-finding: numerical implementations of the affine and projective Buchberger-Möller algorithm (2017)
- Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes: On deflation and multiplicity structure (2017)
- Daleo, Noah S.; Hauenstein, Jonathan D.: Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme (2016)
- Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes: Certifying isolated singular points and their multiplicity structure (2015)
- Batselier, Kim; Dreesen, Philippe; De Moor, Bart: On the null spaces of the Macaulay matrix (2014)
- Griffin, Zachary A.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J.: Numerical computation of the Hilbert function and regularity of a zero dimensional scheme (2014)
- Hao, Wenrui; Sommese, Andrew J.; Zeng, Zhonggang: Algorithm 931, an algorithm and software for computing multiplicity structures at zeros of nonlinear systems (2013)