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A power series method for computing singular solutions to nonlinear analytic systems. (English) Zbl 0756.65079

Given a system of analytic equations having a singular solution, we show how to develop a power series representation for the solution. This series is computable, and when the multiplicity of the solution is small, highly accurate estimates of the solution can be generated for a moderate computational cost.
In this paper, a theorem is proven (using results from several complex variables) which establishes the basis for the approach. Then a specific numerical method is developed, and data from numerical experiments are given.
Reviewer: A.P.Morgan

MSC:

65H10 Numerical computation of solutions to systems of equations
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations

Software:

HOMPACK; PITCON
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Full Text: DOI EuDML

References:

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