FITTING FUNCTIONAL EQUATIONS TO EXPERIMENTAL DATA
Abstract
Much of mathematical analysis is devoted to the problem of predicting the future behavior of a system, given a descriptive equation and the current state. This is surprising since a basic scientific problem in such fields as physics, engineering, biology and economics is that of determining the structure of a system, given various observations over time. Many types of functional equations may be converted into systems of ordinary differential equations. This means that wide classes of direct problems can be solved as initial-value problems. This also means that a great many inverse problems may be computationally resolved. Let the equations which describe a particular process be a system of differential equations. The unknown structure of the process is reflected in unknown system parameters which appear in the differential equations or in the initial conditions. These parameters are to be estimated on the basis of observations of the process. The identification problem takes the form of a nonlinear boundary-value problem. This can be solved by a variety of methods. One that has been shown to be quite effective is described in this report.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1967
- Accession Number
- AD0660553
Entities
People
- Harriet H. Kagiwada
- Robert E. Kalaba
Organizations
- RAND Corporation