An Efficient Way Of Programming Eaves' Fixed Point Algorithm

The recently developed fixed point algorithms have provided the possibility of applying advanced numerical computation procedures in a broad field of economics. In particular, the pioneer work of Scarf [4,5], has shown its importance in the computation of economic equilibria. Moreover, Eaves [3] has succeeded in constructing an algorithm based more or less on the same principles as used by Scarf but providing in general a more efficient way in computing fixed points. Therefore his algorithm may be preferred especially in its application to rather extensive problems. This paper deals with the formulation of Eaves' method such that with a minimum of storage and computation time his algorithm may be prepared for the computer. The algorithm as described i [3] can substantially be improved by reformulating the replacement step and by the application of an efficient inverse routine developed by Bartels [1] on the pivot step. A very concise introduction to fixed point algorithms is given in section 2, where the basic thoughts behind this methods are pictured, omitting for the sake of legibility the mathematical justifications. For those who are interested in the latter aspect we refer to the original publications. In section 3 Eaves' method is considered with an explanation of the replacement step in section 3.1 and its reformulation in section 3.2. Sections 3.3 and 3.4 are dealing with the pivot step and the labeling respectively, while in section 4 a complete FORTRAN computer nrncyra.m of the algorithm is given.