Titlebook: Computing Equilibria and Fixed Points; The Solution of Nonl Zaifu Yang Book 1999 Springer Science+Business Media Dordrecht 1999 economics.e

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First Algorithms for Approximating Fixed Points on the Unit Simplex,r 1, Brouwer theorem guarantees the existence of a fixed point on .. but does not offer any insight about the location of such fixed points. Nevertheless it is clear to us that in order to approximate a fixed point, one possible way is to design a systematic procedure for finding completely labelled

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Variable Dimension Restart Algorithms,th methods we need to imbed an .-dimensional problem into (. + 1)-dimensional space. Moreover, a path of (. + 1)-simplices is generated. In this chapter we will introduce a more efficient algorithm which was developed by van der Laan and Talman [1979]. This algorithm is called the variable dimension

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The Computation of a Continuum of Zero Points of a Point-to-Set Mapping,of fact, most of the existing fixed point theorems only guarantee the existence of a single fixed point. As far as we are aware of, Browder theorem is the only result on the existence of a connected set of fixed points up to now. Recall in Chapter 1 this theorem is stated as follows. Let . be a none

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The Computation of Antipodal Fixed Points,shown in a constructive way that there exists a zero point of . in .. if for every ∈ .(..), . (−.) ≠ .. (−.) for all . > 0. It will be argued that this result is so strong that it implies several powerful fixed point theorems, including Borsuk-Ulam’s theorem and Brouwer’s fixed point theorem. We wil

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,Gröbner Bases for Solving Multivariate Polynomial Equations,attention in the field of symbolic computation and computational algebra. In algebra the famous . states that given . in the set .[..,..., ..] of all polynomials in n variables with coefficients in a field . and an ideal . =< .., ..., .., > of .[..,..., ..], determine whether . is in . or not. Buchb

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