Coefficient-parameter polynomial continuation
Applied Mathematics and Computation
On multiple zeros of systems of algebraic equations
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
A method computing multiple roots of inexact polynomials
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Numerical Polynomial Algebra
Computing the multiplicity structure in solving polynomial systems
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Newton's method with deflation for isolated singularities of polynomial systems
Theoretical Computer Science
A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations
SIAM Journal on Numerical Analysis
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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.