Padé approximation of Stieltjes series
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Using Nuttall's compact formula for the [n, n - 1] Pad'e approximant, the authors show that there is a natural connection between the Padé approximants of a series of Stieltjes and orthogonal polynomials. In particular, we obtain the precise error formulas. The [n, n - 1] Padé approximant in this case is just a Gaussian quadrature of the Stieltjes integral. Hence, analysis of the error is now possible and under very mild conditions it is shown that the [n, n + j], j ≥ - 1, Padé approximants converge to the Stieltjes integral. © 1975.
author list (cited authors)
Allen, G. D., Chui, C. K., Madych, W. R., Narcowich, F. J., & Smith, P. W.