A Practical Guide to Splines

This book is a first introduction to a field of numerical analysis of particular practical importance. Among the topics covered are linear, cubic and parabolic splines, B-splines, piecewise polynomial functions, and specific approximation methods. The book is intended for the engineer or scientist who wishes to develop some expertise in the computational use of splines. Fortran programs can be found throughout the book.

Texte du rabat

This book is based on the author's experience with calculations involving polynomial splines. It presents those parts of the theory that are especially useful in calculations and stresses the representation of splines as weighted sums of B-splines. This revised edition has been typeset, and all figures have been redrawn. In a major change, the B-spline theory is now developed directly from the recurrence relations without recourse to divided differences. Almost all formal statements are now provided with proofs, and many minor changes have been made throughout, including the correction of errors.

Contenu
I · Polynomial Interpolation.- II · Limitations of Polynomial Approximation.- III · Piecewise Linear Approximation.- IV · Piecewise Cubic Interpolation.- V · Best Approximation Properties of Complete Cubic Spline Interpolation and Its Error.- VI · Parabolic Spline Interpolation.- VII · A Representation for Piecewise Polynomial Functions.- VIII · The Spaces ?