The optimum approximation of an orthogonal expansion having bounded higher order correlations of stochastic coefficients

摘要

In this paper, we establish the optimum interpolation approximation for a set of multi-dimensional statistical orthogonal expansions. Each signal has a bounded linear combination of higher order self-correlations and mutual-correlations with respect to coefficients of the expansion. For this set of signals, we present the optimum interpolation approximation that minimizes various worst-case measures of mean-square error among all the linear and the nonlinear approximations. Finally, as a practical application of the optimum interpolation approximation, we present a discrete numerical solution of linear partial differential equations with two independent variables.