Showing papers on "Monotone cubic interpolation published in 1969"

Exponential spline interpolation

Abstract: Piecewise cubic polynomial spline interpolation [3] or smoothing [4] often gives undesirable inflexion points. We describe a spline interpolation method that allows to avoid these inflexion points and contains cubic splines as special case. The method is a generalization of the work in [2]. The proof of the theorem motivating the use of exponential splines is simplified. An ALGOL procedure is presented that allows to mix piecewise cubic and exponential spline interpolation suitably.

Bicubic Spline Interpolation as a Method for Treatment of Potential Field Data

Abstract: A method for the generation of bicubic spline functions is presented in this paper. From this method it becomes apparent that these functions derive their potential strength in accurate and reliable representation of two‐dimensional data by maintaining continuity of the variable and its slope and curvature throughout the area of observation. The results obtained by computing horizontal and vertical derivatives with model and field data illustrate the exceptional accuracy achieved with spline functions. The piecewise cubic polynomial functions expressing observed data analytically in space are used to estimate amplitude and phase spectra of magnetic anomalies. At relatively long wavelengths the amplitude spectrum thus calculated displays remarkable similarity with the true spectrum and is found to be superior to that obtained with two‐dimensional Fourier series expansion. A cubic spline method is also presented for computing values of an observed variable at equispaced points along two orthogonal direction...

Errors in cubic spline interpolation

Abstract: This paper deals with the problem of finding error bounds for cubic spline interpolation of functions of the classC 4[a, b], andC 5[a, b], by examining a relationship between cubic spline interpolation and piecewise cubic Hermitian interpolation. The method also gives an indication of what happens, in the case of almost uniform meshes, especially if the approximated function is in the classC 5[a, b]. Comparison is made with recent work carried out by K. E. Atkinson [3], in dealing with natural cubic spline interpolation.

Error bounds for periodic quintic splines

Abstract: Explicit error bounds for periodic quintic spline interpolation are developed. The first (third) derivative of the periodic spline is shown to be a sixth (fourth) order approximation at the mesh points to the first (third) derivative of the function being interpolated.