AN ALGORITHM FOR FINDING RATIONAL APPROXIMATIONS
AIR FORCE CAMBRIDGE RESEARCH LABS HANSCOM AFB MA
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A rational approximation to a function provides a rapid and convenient way to calculate numerical values of the function to within a predetermined error. The question of how to find rational approximations to given functions is considered. Definitions of terms, a precise statement of what the criterion of best fit is, and statements of some classical results are given. Two closely related iterative methods for finding best rational approximations are defined. A proof of convergence of these methods is given for a special case in which both methods are the over same, and these methods are compared with some others. Some results obtained by one of the iterative methods are presented, together with a brief description of the computer program used to obtain them.
- Numerical Mathematics