Chebyshev Expansions and Rational Approximations for Some Special Functions and Analytic Continuation Formulas for These Special Functions,
MISSOURI UNIV KANSAS CITY DEPT OF MATHEMATICS
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Let Az A sub mz a sub mz sup mBz,m where A sub mz is a polynomial in z of degree m-1. Suppose Az and Bz,m are approximated by main diagonal Pade approximations of order n and r respectively. Suppose that the number of operations needed to evaluate both sides of the above equations by means of the Pade approximations and polynomial noted are the same. Thus 4n 3m 4r. We address ourselves to the question of which procedure is more efficient. That is, which procedure produces the smallest error. A variant of this problem is the situation where Az and Bz,m are approximated by their representations in infinite series of Chebyshev polynomials of the first kind truncated after n and r terms respectively. Here n mr.
- Theoretical Mathematics