This paper introduces random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs). We prove that these algorithms succeed in breaking the curse of dimensionality for a...

This paper presents a procedure for clustering analysis that combines Kohone’s Self organizing Feature Map (SOFM) and statistical schemes. The idea is to cluster the data in two stages: run SOFM and then minimize the segmentation dispersion. The advantages of proposed procedure will be...

This paper compares the performance of the Howard (1960) policy iteration algorithm for infinite-horizon continuous-state Markovian decision processes (MDP's) using alternative random, quasi- random, and deterministic discretizations of the state space, or grids. Each grid corresponds to an...

We consider the problem of computing approximations to fixed points of quasilinear contraction mappings defined on the space of continuous functions of $d$ variables. Our main emphasis is on large d. Examples of such mappings include the Bellman operator from the theory of dynamic programming....

This essay is a response to a growing negative literature that suggests that neoclassical economic theories based on hypotheses of rationality and equilibrium are of limited practical relevance because they require an infeasibly large number of calculations. Many of the negative results are...