Invariant Imbedding and the Variational Treatment of Fredholm Integral Equations with Displacement Kernels.

by J. L. Casti, Robert E. Kalaba, S. Ueno


Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback0.245 pages $20.00 $16.00 20% Web Discount

A new and computationally efficient method of solving Fredholm integral equations with displacement kernels, such as those arising in radiative transfer and optimal filtering theory. Frequently, studies of these equations are based on the fact that their solutions minimize certain quadratic functionals, which opens the way to the employment of the Rayleigh-Ritz method. The aim of the present study is radically different: It is shown that the minimizer of the quadratic functional satisfies a Cauchy problem. The numerical integration of the initial-value problem is carried out by replacing the integrals by finite sums using gaussian quadrature formulas. This reduces the differential-integral equations to a system of ordinary differential equations. 17 pp. Refs. (MW)

This report is part of the RAND Corporation Research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.