Spencer D. Shellman

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In this paper we present a new algorithm for the two-dimensional fixed point problem f(x)=x on the domain [0, 1]×[0, 1], where f is a Lipschitz continuous function with respect to the infinity norm, with constant 1. The computed approximation x̃ satisfies ||f(x̃)− x̃||. [ e for a specified tolerance e < 0.5. The upper bound on the number of required(More)
We present the PFix algorithm for the fixed point problem f ðxÞ 1⁄4 x on a nonempty domain 1⁄2a; b ; where dX1; a; bAR ; and f is a Lipschitz continuous function with respect to the infinity norm, with constant qp1: The computed approximation x̃ satisfies the residual criterion jj f ðx̃Þ x̃jjNpe; where e40: In general, the algorithm requires no more than Pd(More)
We present the PFix algorithm for approximating a fixed point of a function f that has arbitrary dimensionality, is defined on a rectangular domain, and is Lipschitz continuous with respect to the infinity norm with constant 1. PFix has applications in economics, game theory, and the solution of partial differential equations. PFix computes an approximation(More)
We present the BEDFix (Bisection Envelope Deep-cut Fixed point) algorithm for the problem of approximating a fixed point of a function of two variables. The function must be Lipschitz continuous with constant 1 with respect to the infinity norm; such functions are commonly found in economics and game theory. The computed approximation satisfies a residual(More)
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