How high-precision calculations can stimulate mathematical research

DOI10.1016/0168-9274(92)90040-KzbMath0758.65001OpenAlexW2082282335MaRDI QIDQ1195358

Richard S. Varga

Publication date: 25 October 1992

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(92)90040-k

zbMATH Keywords

rational approximationBernstein conjecturebest local rational approximationChebyshev semi-discrete rational approximationhigh-precision calculationsPadé rational matrix approximations of the matrix exponential

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Best approximation, Chebyshev systems (41A50) Approximation by rational functions (41A20) Algorithms for approximation of functions (65D15) History of numerical analysis (65-03) History of approximations and expansions (41-03)

Uses Software

• Algorithm 524

Cites Work

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• Asymptotics of diagonal Hermite-Padé polynomials
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• Orthogonal polynomials with complex-valued weight function. II
• Zur rationalen Approximierbarkeit von \(e^{-x}\) über \([0, \infty)\)
• Rational approximation to \(|x|\)
• Chebyshev rational approximations to \(e^{-x}\) in \([0,+\infty)\) and applications to heat-conduction problems
• The Carathéodory–Fejér Method for Real Rational Approximation
• On Higher Order Stable Implicit Methods for Solving Parabolic Partial Differential Equations
• Rational Approximation to $e^{ - x} $ and Related $\mathcal{L}^2 $-Problems
• EQUILIBRIUM DISTRIBUTIONS AND DEGREE OF RATIONAL APPROXIMATION OF ANALYTIC FUNCTIONS
• ON THE LEAST DEVIATIONS OF THE FUNCTION $ \operatorname{sign} x$ AND ITS PRIMITIVES FROM THE RATIONAL FUNCTIONS IN THE $ L_p$ METRICS, $ 0 < p \leqslant \infty$
• Best uniform rational approximation of 𝑥^{𝛼} on [0,1]
• ESTIMATES OF THE GROWTH OF RATIONAL FUNCTIONS AND SOME OF THEIR APPLICATIONS
• ASYMPTOTICS FOR LEAST DEVIATION OF $ \vert x\vert$ FROM RATIONAL FUNCTIONS

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