On the Osculatory Rational Interpolation Problem
نویسنده
چکیده
The problem of the existence and construction of a table of osculating rational functins fj m for 1, m > 0 is considered. First, a survey is given of some results from the theory of osculatory rational interpolation of order s¡ — 1 at points x¡ for i > 0. Using these results, we prove the existence of continued fractions of the form c0 + c, -(x y0) + . . . + ck-(x y0) . . . (x yk_x) ck + l •<* y0) • • ■(* y0\ ck + 2,(.x ~>"fc+l)| + l-1-+ |-Vwith the yk suitably selected from among the x-, whose convergents form the elements rk 0' rk+l 0' rk+l I' rk + 2 ].>••• of the table. The properties of these continued fractions make it possible to derive an algorithm for constructing their coefficients c¡ for í > 0. This algorithm is a generalization of the qd-algorithm.
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