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Quadratically Convergent Methods for the Computation of Unfolded Singularities

P. Kunkel
SIAM Journal on Numerical Analysis
Vol. 25, No. 6 (Dec., 1988), pp. 1392-1408
Stable URL: http://www.jstor.org/stable/2157494
Page Count: 17
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Quadratically Convergent Methods for the Computation of Unfolded Singularities
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Abstract

An underdetermined system of equations for the determination of the Lyapunov-Schmidt reduction is presented. This system can easily be extended to an augmented system for the computation of nontrivial singularities by adding suitable equations, which characterize the singularity. Necessary and sufficient conditions for these additional equations are given, so that the corresponding Gauss-Newton method converges locally and quadratically. For several types of singularities possible equations are derived from invariance conditions. Numerical examples illustrating the results are included.

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