On the convergence of generalized Padé approximants

DOI10.1007/BF01889608zbMath0686.41013MaRDI QIDQ1262488

Herbert R. Stahl

Publication date: 1989

Published in: Constructive Approximation (Search for Journal in Brave)

zbMATH Keywords

singular pointsalgebraic functionsinterpolating rationals

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Padé approximation (41A21) Rate of convergence, degree of approximation (41A25)

Related Items (12)

Padé approximants for functions with branch points -- strong asymptotics of Nuttall-Stahl polynomials ⋮ Convergent interpolation to Cauchy integrals over analytic arcs ⋮ The convergence of Padé approximants to functions with branch points ⋮ The convergence of diagonal Padé approximants and the Padé conjecture ⋮ Padé approximants to certain elliptic-type functions ⋮ Critical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomials ⋮ Weighted extremal domains and best rational approximation ⋮ Distribution of interpolation points of maximally convergent multipoint Padé approximants ⋮ Multipoint Padé approximants to complex Cauchy transforms with polar singularities ⋮ Homogenization of Poisson's kernel and applications to boundary control ⋮ Lippmann–Schwinger–Lanczos algorithm for inverse scattering problems ⋮ On the convergence of bounded \(J\)-fractions on the resolvent set of the corresponding second order difference operator

Cites Work

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• Orthogonal polynomials with complex-valued weight function. I
• Orthogonal polynomials with complex-valued weight function. II
• Divergence of complex rational approximations
• The convergence of Padé approximants of meromorphic functions
• An extension of Montessus de Ballore's theorem on the convergence of interpolating rational functions
• Padé approximants and convergence in capacity
• Extremal domains associated with an analytic function II
• ON MARKOV'S THEOREM FOR MULTIPOINT PADÉ APPROXIMANTS
• ON THE CONVERGENCE OF PADÉ APPROXIMANTS IN CLASSES OF HOLOMORPHlC FUNCTIONS
• On convergence in capacity
• ON THE CONVERGENCE OF GENERALIZED PADÉ APPROXIMANTS OF MEROMORPHIC FUNCTIONS

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