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Bounding Sets in Function Spaces with Applications to Nonlinear Operator Equations

R. E. Moore
SIAM Review
Vol. 20, No. 3 (Jul., 1978), pp. 492-512
Stable URL: http://www.jstor.org/stable/2030352
Page Count: 21
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Bounding Sets in Function Spaces with Applications to Nonlinear Operator Equations
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Abstract

We can compute with bounding sets of numbers, vectors, or functions using the techniques of interval mathematics. The techniques can be used to computationally verify sufficient conditions for existence, uniqueness, and convergence and to construct upper and lower bounds on solutions of nonlinear operator equations. Rounding errors are taken into account. We can compute with set-valued functions and operators on them. The techniques are also useful in search procedures for finding safe starting regions for iterative methods and for constructing natural stopping criteria.

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