APPROXIMATION FORMULA FOR PHYSICAL DATA,

The basic assumption in the paper is that physical data used in high speed computations should have an approximation formula in those cases where the data represents a functional relationship. The ideal solution would be for every such table of data to be accompanied by an appropriate approximation formula. This situation is not likely to be reached for some time, so this paper has investigated the possibility of developing a black box to produce these approximation formulas easily. A computer program to serve as the black box is outlined in the preceding section. It is believed that such a program would be a very adequate tool for the scientist who needs an approximation formula. The major difficulty in the realization of this program is the difficulty of computing approximations by rational functions. This is a formidable mathematical problem, one which is beginning to be understood fully only very recently. These difficulties are discussed in some detail in the appendix. The programming and analytical effort required to develop the computer program outlined in the preceding section is rather large. It depends considerably on the analysts familiarity with the techniques and procedures of approximation theory. Author