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 - 2013/10/21

Y1 - 2013/10/21

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.

UR - http://www.scopus.com/inward/record.url?scp=84885589983&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885589983&partnerID=8YFLogxK

U2 - 10.1145/2513109.2513114

DO - 10.1145/2513109.2513114

M3 - Article

AN - SCOPUS:84885589983

VL - 40

JO - ACM Transactions on Mathematical Software

JF - ACM Transactions on Mathematical Software

SN - 0098-3500

IS - 1

M1 - 5

ER -