Spline interpolation and best quadrature formulae

Best Error Bounds of Quartic Spline Interpolation

In this paper, we have obtained existence, uniqueness, best error bound and convergence properties of C Deficient Quartic Spline Interpolation. Classification Code Ø 41A05, 65D07.

UNIQUENESS OF BEST PARAMETRIC INTERPOLATION BY CUBIC SPLINE CURVES by

Best parametric spline interpolation extends and refines the classical spline problem of best interpolation to (∗) inf t inf f { ∫ 1 0 ‖f (t)‖dt : f(ti) = yi, 1 ≤ i ≤ n} Here t : 0 = t1 < . . . < tn = 1 denotes a sequence of nodes and yi data in R d with y i 6= y i+1 . The R valued functionsf(t) lie componentwise in the Sobolev space L2(0, 1) and ‖ ‖ denotes the Euclidean norm in R. This proble...

Error Propagation by Use of Interpolation Formulae and Quadrature Rules Which Are Computed Numerically

Quadrature formulae for Fourier coefficients

We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Michhelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a func...

Subperiodic trigonometric interpolation and quadrature

We study theoretically and numerically trigonometric interpolation on symmetric subintervals of [−π, π], based on a family of Chebyshevlike angular nodes (subperiodic interpolation). Their Lebesgue constant increases logarithmically in the degree, and the associated Fejérlike trigonometric quadrature formula has positive weights. Applications are given to the computation of the equilibrium meas...