I. J. Schoenberg
CBMS-NSF Regional Conference Series in Applied Mathematics 12
As this monograph shows, the purpose of cardinal spline interpolation is to bridge the gap between the linear spline and the cardinal series. The author explains cardinal spline functions, the basic properties of B-splines, including B- splines with equidistant knots and cardinal splines represented in terms of B-splines, and exponential Euler splines, leading to the most important case and central problem of the book-- cardinal spline interpolation, with main results, proofs, and some applications. Other topics discussed include cardinal Hermite interpolation, semi-cardinal interpolation, finite spline interpolation problems, extremum and limit properties, equidistant spline interpolation applied to approximations of Fourier transforms, and the smoothing of histograms.
The Basis Property of B-splines; The Exponential Euler Splines; Cardinal Spline Interpolation; Cardinal Hermite Interpolation; Other Spaces and Semi-Cardinal Interpolation; Finite Spline Interpolation Problems; Semi-Cardinal Interpolation and Quadratures with General Boundary Conditions; Extremum and Limit Properties; Applications: Approximations of Fourier Transforms and the Smoothing of Histograms.
1973 / vi + 125 pages / Softcover / ISBN-13: 978-0-898710-09-0 / ISBN-10: 0-89871-009-X /
List Price $45.00 / SIAM/CBMS Member $31.50 / Order Code CB12