ON THE APPROXIMATION OF CURVES BY LINE SEGMENTS USING DYNAMIC PROGRAMMING. II
Abstract
The technique of dynamic programming is applied to approximate a given continuous function g(x) by a finite number of line segments over the interval a,b . The problem is to determine the constants a sub k, b sub k, k equals 0,..., N - 1 and the points of division u sub 1,..., u sub N-1 in the interval a,b that minimize the function J = N-1k=0 uk+1 (g(x) - a - b x)2dx.k kku Results are calculated for g equals e-x by means of a FORTRAN program for the IBM-7090. An analytic treatment is given of the functions g(x) equals x squared and g(x) equals 1/e to the cx power that is easily derived by utilizing the functional equation technique of dynamic programming. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1962
- Accession Number
- AD0272143
Entities
People
- Bella Kotkin
- Richard E. Bellman
Organizations
- RAND Corporation