Abstract
Rational interpolation problems for functions having numerator degree higher than denominator degree are connected with solutions of systems of equations the coefficient matrix of which has a mixed structure: the first columns are of Vandermonde type whereas the last columns form a Löwner matrix. Here three-term recursions for the rational interpolants are developed which can be translated into recurrence formulas for the solutions of homogeneous systems with such a coefficient matrix. On this base an O( n 2) algorithm for the solution of n× n nonhomogeneous Löwner–Vandermonde systems is obtained.
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