TY - JOUR
T1 - Algorithm 931
T2 - An algorithm and software for computing multiplicity structures at zeros of nonlinear systems
AU - Hao, Wenrui
AU - Sommese, Andrew J.
AU - Zeng, Zhonggang
PY - 2013
Y1 - 2013
N2 - 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 equationby- 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.
AB - 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 equationby- 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.
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U2 - 10.1145/2513109.2513114
DO - 10.1145/2513109.2513114
M3 - Article
AN - SCOPUS:84885589983
SN - 0098-3500
VL - 40
JO - ACM Transactions on Mathematical Software
JF - ACM Transactions on Mathematical Software
IS - 1
M1 - 5
ER -