The general recurrence relation for divided differences and the general Newton-interpolation-algorithm. With applications to trigonometric interpolation

DOI10.1007/BF01401043zbMath0427.65004MaRDI QIDQ1136470

Günter W. Mühlbach

Publication date: 1979

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132618

zbMATH Keywords

algorithmnumerical exampletrigonometric interpolationChebyshev-systemNewton-like interpolation formulaNewton's classical interpolation formularecurrence relation for divided differences

Mathematics Subject Classification ID

Trigonometric interpolation (42A15) Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Numerical methods for trigonometric approximation and interpolation (65T40)

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Determinants and the structure of the integral approximant table ⋮ Linear extrapolation by rational functions, exponentials and logarithmic functions ⋮ Interpolation mixing hyperbolic functions and polynomials ⋮ A general extrapolation procedure revisited ⋮ Elimination techniques and interpolation ⋮ On multivariate interpolation by generalized polynomials on subsets of grids ⋮ New mapped unequal-sized trigonometric WENO scheme for hyperbolic conservation laws ⋮ A new type of increasingly high-order multi-resolution trigonometric WENO schemes for hyperbolic conservation laws and highly oscillatory problems ⋮ Remarks on a unified theory for classical and generalized interpolation and extrapolation ⋮ A general recurrence interpolation formula and its applications to multivariate interpolation ⋮ A representation of the interpolation polynomial ⋮ A New Fifth-Order Trigonometric WENO Scheme for Hyperbolic Conservation Laws and Highly Oscillatory Problems ⋮ Interpolation on cycloidal spaces ⋮ Note on trigonometric divided differences ⋮ On the comparison of four different implementations of a third-order ENO scheme of box type for the computation of compressible flow ⋮ Baryzentrische Formeln zur Trigonometrischen Interpolation. I

Cites Work

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• The general Neville-Aitken-algorithm and some applications
• A recurrence formula for generalized divided differences and some applications
• Divided differences for functions of two variables for irregularly spaces arguments
• Newton‐ und Hermite‐Interpolation mit Čebyšev‐Systemen

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