Abstract
In this paper Chebyshev best fit approximations by rational functions are given to the functionsln, exp, sin, cos andarctan. The approximations are presented in two ways: by a Thiele-type fraction and by a Jacobi-fraction. While the Thielefractions are time consuming, but well behaved with respect to error propagation, the Jacobi-fractions are extremely fast in evaluation, but need provision for some guard digits to preserve the full precision of approximation. Error propagation and stability have been tested by several methods, e.g. using the TRIPLEX MAINZ S 2002Algol Compiler version implemented by N. Krier. The approximations presented here are a part of a CONTROL DATA 3300 FORTRAN Double REAL subsystem, where they run successfully. Higher precision approximations up to 40 decimal places using the same method are available from the author. In the model procedures given in the following it is understood that real arithmetic as well as integer arithmetic and the standard functions used work on operands of one same (extended) length.
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