Improved validated bounds for Taylor coefficients and for Taylor remainder series

DOI10.1016/S0377-0427(02)00719-7zbMath1018.65030MaRDI QIDQ1872963

Markus Neher

Publication date: 19 May 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical examplesarithmeticmathematical softwareenclosure methodscomplex intervalbounds for Taylor coefficients of analytic functions

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Power series (including lacunary series) in one complex variable (30B10) Computation of special functions and constants, construction of tables (65D20) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Algorithms with automatic result verification (65G20) Packaged methods for numerical algorithms (65Y15) Software, source code, etc. for problems pertaining to functions of a complex variable (30-04)

Related Items (5)

Effective approximation of the solutions of algebraic equations ⋮ Verified integration of linear \(n\)th order ODEs using large steps ⋮ Taylor's expansion revisited: a general formula for the remainder ⋮ Effective bounds for P-recursive sequences ⋮ Truncation bounds for differentially finite series

Uses Software

• ACETAF
• C-XSC
• C-XSC 2.0
• INTOPT_90
• filib++

Cites Work

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• Derived eigenvalues of symmetric matrices, with applications to distance geometry
• Automatic differentiation: techniques and applications
• Rigorous global search: continuous problems
• Berechenbare Schranken von Taylorkoeffizienten analytischer Funktionen
• Bounding the Solution of Interval Linear Equations
• ACETAF
• On factorization of analytic functions and its verification
• Validated bounds for Taylor coefficients of analytic functions

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