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.
Author(s): I. J. Schoenberg
Series: CBMS-NSF Regional Conference Series in Applied Mathematics
Publisher: Society for Industrial Mathematics
Year: 1987
Language: English
Pages: 134
Cardinal Spline Interpolation......Page 3
Contents......Page 5
An Homage to Leonard Euler......Page 6
Preface......Page 7
Lecture 1 Introduction, Background and Examples......Page 9
Lecture 2 The Basis Property of B-Splines......Page 19
Lecture 3 The Exponential Euler Splines......Page 29
Lecture 4 Cardinal Spline Interpolation......Page 41
Lecture 5 Cardinal Hermite Interpolation......Page 51
Lecture 6 Other Spaces and Semi-Cardinal Interpolation......Page 67
Lecture 7 Finite Spline Interpolation Problems......Page 79
Lecture 8 Semi-Cardinal Interpolation and Quadratures with General Boundary Conditions......Page 93
Lecture 9 Extremum and Limit Properties......Page 103
Lecture 10 Applications: 1. Approximations of Fourier Transforms. 2. The Smoothing of Histograms......Page 117
References......Page 129
