Newton's method and a surface with Jacobian zero

E. I. Lin'kov

Moscow Region Pedagogical Instityte

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.

UDC: 517.392

Received: 08.07.1974

 English version: Mathematical Notes, 1975, 18:2, 738–742

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