Summary
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.
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Morgan, A.P., Sommese, A.J. & Wampler, C.W. A power series method for computing singular solutions to nonlinear analytic systems. Numer. Math. 63, 391–409 (1992). https://doi.org/10.1007/BF01385867
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DOI: https://doi.org/10.1007/BF01385867