The QD-Algorithm for Padé-Approximants in Operator Theory
Copyright policy )The QD-Algorithm for Padé-Approximants in Operator Theory
For real functions on \(R^ 1\) which are analytic at the origin it is well known that the Padé approximants can be constructed from the quotient-difference algorithm. In her Ph.D. thesis [University of Antwerp, Belgium (1982), see also SIAM J. Math. Anal. 14, 1009-1014 (1983; Zbl 0538.65036)] the author introduced Padé approximants for operators F:X\(\to Y\) between a Banach space X and a commutative Banach algebra Y which are analytic in some open ball centered at the origin. In this paper, an abstract version of the QD-algorithm is formulated in analogy with the one-dimensional case, and it is shown that once again the (abstract) Padé approximants can be constructed from it as convergents of a continued fraction.
- University of Antwerp Belgium
quotient difference algorithm, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Banach space, Numerical solutions to equations with nonlinear operators, commutative Banach algebra, Padé approximation, Mathematics, QD-algorithm, continued fraction
quotient difference algorithm, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Banach space, Numerical solutions to equations with nonlinear operators, commutative Banach algebra, Padé approximation, Mathematics, QD-algorithm, continued fraction
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