A NOTE ON NONLINEAR SUMMABILITY TECHNIQUES IN INVARIANT IMBEDDING
Abstract
The use of principles of invariance, as in invariant imbedding and dynamic programming, leads characteristically to functional equations of the form fn+1(p) = Tn(fn(g(p))), n = 0,1,2,..., where f0(p) is known. The computational solution proceeds stagewise, with f1 determined from a knowledge of f0, f2 determined by f1, and so on. In general, what is desired is the transient behvaior, small n, and the steady-state, or asymptotic behavior as n . In a number of significant processes--radiative transfer, control theory, inventory theory, and Markovian decision processes in general--only the asymptotic results are of interest. This is also the case in the application of gradient techniques. The application of nonlinear summability techniques to radiative transfer is outlined.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1963
- Accession Number
- AD0296925
Entities
People
- Richard E. Bellman
- Robert E. Kalaba
Organizations
- RAND Corporation