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Padé approximation and orthogonal polynomials

Published online by Cambridge University Press:  17 April 2009

G.D. Allen ,
C.K. Chui ,
W.R. Madych ,
F.J. Narcowich  and
P.W. Smith
G.D. Allen
Affiliation:
Department of Mathematics, Texas A&M University, College of Science, Texas, USA.
C.K. Chui
Affiliation:
Department of Mathematics, Texas A&M University, College of Science, Texas, USA.
W.R. Madych
Affiliation:
Department of Mathematics, Texas A&M University, College of Science, Texas, USA.
F.J. Narcowich
Affiliation:
Department of Mathematics, Texas A&M University, College of Science, Texas, USA.
P.W. Smith
Affiliation:
Department of Mathematics, Texas A&M University, College of Science, Texas, USA.
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By using a variational method, we study the structure of the Padé table for a formal power series. For series of Stieltjes, this method is employed to study the relations of the Padé approximants with orthogonal polynomials and gaussian quadrature formulas. Hence, we can study convergence, precise locations of poles and zeros, monotonicity, and so on, of these approximants. Our methods have nothing to do with determinant theory and the theory of continued fractions which were used extensively in the past.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 2 , April 1974 , pp. 263 - 270
Copyright
Copyright © Australian Mathematical Society 1974

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