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Solving discrete zero point problems

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Author Info
Laan, G. van der
Talman, A.J.J.
Yang, Z. (Tilburg University, Center for Economic Research)

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Abstract

In this paper an algorithm is proposed to .nd a discrete zero point of a function on the collection of integral points in the n-dimensional Euclidean space IRn. Starting with a given integral point, the algorithm generates a .nite sequence of adjacent integral simplices of varying dimension and terminates with, under certain convergency conditions, a vertex, which yields a discrete zero point of the function under consideration.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 113.

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Date of creation: 2004
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Handle: RePEc:dgr:kubcen:2004113

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  1. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part I: Generalities," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January. [Downloadable!] (restricted)
  2. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation, Yale University. [Downloadable!]
  3. Iimura, Takuya, 2003. "A discrete fixed point theorem and its applications," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 725-742, September. [Downloadable!] (restricted)
  4. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November. [Downloadable!] (restricted)
  5. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2002. "Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies," Journal of Economic Theory, Elsevier, vol. 103(2), pages 411-428, April. [Downloadable!] (restricted)
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  1. Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2007. "Combinatorial Integer Labeling Thorems on Finite Sets with an Application to Discrete Systems of Nonlinear Equations," Discussion Paper 2007-88, Tilburg University, Center for Economic Research. [Downloadable!]
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  2. Gerard van der Laan & Dolf Talman & Zaifu Yang, 2005. "Solving Discrete Zero Point Problems with Vector Labeling," Tinbergen Institute Discussion Papers 05-106/1, Tinbergen Institute. [Downloadable!]
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