On measures of ill-conditioning for nonlinear equations
Author:
Werner C. Rheinboldt
Journal:
Math. Comp. 30 (1976), 104-111
MSC:
Primary 65J05
DOI:
https://doi.org/10.1090/S0025-5718-1976-0400702-1
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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- J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York-London, 1970. MR 0273810
- R. S. Varga, Functional analysis and approximation theory in numerical analysis, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1971. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 3. MR 0310504
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Article copyright:
© Copyright 1976
American Mathematical Society