A Practical Guide to Splines

A Practical Guide to Splines by De Boor, Carl. paperback edition. ISBN: 9780387903569.

This book (seventh printing) is based on the authors experience with calculations involving polynomial splines. It presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines. After two chapters summarizing polynomial approximation, a rigorous discussion of elementary spline theory is given involving linear, cubic and parabolic splines. The computational handling of piecewise polynomial functions (of one variable) of arbitrary order is the subject of chapters 7 and 8, while chapters 9, 10, and 11 are devoted to B-splines. The distances from splines with fixed and with variable knots is discussed in chapter 12. The remaining five chapters concern specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.