Theory of minimal splines (Q2755083)

This book presents a systematic introduction to minimal splines, where estimates of corresponding approximation constants are of special interest. Numerical methods and applications are not discussed in detail. Roughly spoken, minimal splines are special functions with small supports and can be considered as a generalization of the well-known polynomial \(B\)-splines. Therefore, minimal splines have similar properties as \(B\)-splines.NEWLINENEWLINE In Chapter 1, the theory of minimal (Lagrange and Hermite) interpolation splines is presented. Boundary minimal splines and corresponding quadrature formulas are considered in Chapter 2. Trigonometric minimal splines are studied in Chapter 3. The Chapters 4 and 5 are devoted to smooth minimal splines. Chapter 6 presents estimates of approximation constants for minimal splines. The Chapters 7--9 treat a generalization of minimal splines.