科研之友
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摘要
We consider the classical problem of finding the best uniform approximation by polynomials of 1/(x - a)(2), where a %26gt; 1 is given, on the interval [-1, 1]. First, using symbolic computation tools we derive the explicit expressions of the polynomials of best approximation of low degrees and then give a parametric solution of the problem in terms of elliptic functions. Symbolic computation is invoked then once more to derive a recurrence relation for the coefficients of the polynomials of best uniform approximation based on a Pell-type equation satisfied by the solutions.
- 出版日期2014
