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Mathematics of Computation

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On measures of ill-conditioning for nonlinear equations

Author: Werner C. Rheinboldt
Journal: Math. Comp. 30 (1976), 104-111
MSC: Primary 65J05
MathSciNet review: 0400702
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Abstract: Let $ {x^\ast}$ be a solution of the nonlinear equation $ Fx = b$ on a normed linear space and $ {y^\ast}$ that of a perturbed equation $ Gx = c$. Estimates for the relativized error between $ {x^\ast}$ and $ {y^\ast}$ are derived which extend a known estimate for the corresponding matrix case. The condition number of F depends now also on the domain, and special considerations are needed to determine the existence of the solution of the perturbed equation. For differentiable F, when the domain shrinks to a point, the condition number of F is shown to reduce to that of the derivative at that point.

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Article copyright: © Copyright 1976 American Mathematical Society