Approximation of Analytic Functions: A Method of Enhanced Convergence

DOI10.2307/2153569zbMath0806.65018OpenAlexW2055195470MaRDI QIDQ4305974

Oscar P. Bruno, Fernando Reitich

Publication date: 15 September 1994

Full work available at URL: https://doi.org/10.2307/2153569

zbMATH Keywords

Padé approximationsanalytic functionsTaylor expansionconformal transformationswave scatteringEuler transformmethod of enhanced convergence

Mathematics Subject Classification ID

Power series (including lacunary series) in one complex variable (30B10) Approximation in the complex plane (30E10) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical summation of series (65B10)

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Cites Work

• An investigation of the applicability of the Padé approximant method
• The practical use of the Euler transformation
• Computations of coefficients in the polynomials of Padé approximations by solving systems of linear equations
• Convergence acceleration on a general class of power series
• Algebraic Computations of Scaled Padé Fractions
• Procedures for Estimating the Error in Pade Approximation
• On Stable Calculation of Linear Functionals
• On Generating Orthogonal Polynomials
• Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain
• The condition of gram matrices and related problems
• Construction of Gauss-Christoffel Quadrature Formulas
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