Contraction mappings in interval analysis
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Under certain conditions, the contraction mapping fixed point theorem guarantees the convergence of the iterationxi+1=f(x i ) toward a fixed point of the functionf:Rn →Rn. When an interval extensionF off is used in a similar iteration scheme to obtain a sequence of interval vectors these conditions need not provide convergence to a degenerate interval vector representing the fixed point, even if the width of the initial interval vector is chosen arbitrarily small. We give a sufficient condition on the extensionF in order that the convergence is guaranteed. The centered form of Moore satisfies this condition.
KeywordsComputational Mathematic Point Theorem Fixed Point Theorem Contraction Mapping Interval Analysis
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- 1.J. M. Ortega, W. C. Reinboldt,Iterative solution of nonlinear equations in several variables, Academic Press, 1970.Google Scholar
- 2.R. E. Moore,Interval Analysis, Prentice-Hall, 1966.Google Scholar
- 3.E. R. Hansen,Topics in Interval Analysis, Oxford University Press, 1969.Google Scholar
- 4.E. R. Hansen,A generalized interval arithmetic, inInterval Mathematics, ed. K. Nickel, Springer Verlag, 1975.Google Scholar