Newton's method and a surface with Jacobian zero |
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Authors: | E I Lin'kov |
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Institution: | 1. Moscow Regional Pedagogical Institute, USSR
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Abstract: | Suppose a system of nonlinear real equations P(x)=0, where P and x are n-dimensional vectors, is solved by means of the continuous analog of Newton's method. We study the behavior of the method near the surface S with Jacobian zero: S={x¦det P′(x)=0}. A computational strategy is suggested in the case where the method diverges. |
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