A Combinatorial Interpretation of the Quotient-Difference Algorithm

Xavier Gérard Viennot ()
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Xavier Gérard Viennot: Université Bordeaux I, LaBRI et CNRS

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 379-390 from Springer

Abstract: Abstract During the last thirty years, a growing interest for Padé approximants appeared in many theoretical and applied fields, such as numerical analysis, theoretical physics, chemistry, electronics, … as shown in the books Baker [1], Baker, Graves-Morris [2], Brezinski [3], Gilewicz [11]. Padé approximants are strongly connected with continued fractions (see for example Henrici [16], Jones, Thron [17], Wall [25]) and orthogonal polynomials (see for example Brezinski [4, 5], Draux [7], Van Rossum [22], Wynn [26]). The so-called quotient-difference algorithm, or qd-algorithm, plays an important role in these theories. It was originated in Steifel [21] and studied by Rutishauser [19], Henrici [16,15]. (See also Brezinski [5], Gragg [12]).

Keywords: Orthogonal Polynomial; Continue Fraction; Young Tableau; Elementary Step; Catalan Number (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-3-662-04166-6_34

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