Approximation With Taylor Matching At The Origin

Robust techniques for best approximation by polynomials matching up to given order the Taylor series at {0} are given. Much cheaper robust techniques giving near best results in favorable cases are also given for the same problems. A heuristic technique for matching only the function value at {0} when it is an error extremum is put on a sound theoretical basis and offers possibilities of making rounding error and analytic error cancel, thus reducing their effect.

Keywords:

• Polynomial Matching Taylor Series
• Best Approximation
• Remez Algorithm
• Monic Polynomials Of Least Norm
• Heuristic