This book is based on the author’s experience with calculations involving polynomial splines, presenting those parts of the theory especially useful in calculations and stressing the representation of splines as weighted sums of B-splines. The B-spline theory is developed directly from the recurrence relations without recourse to divided differences. This reprint includes redrawn figures, and most formal statements are accompanied by proofs.
Author(s): Carl De Boor
Series: Applied Mathematical Sciences 27
Publisher: Springer
Year: 2001
Language: English
Pages: 366
Tags: Математика;Вычислительная математика;
Preface......Page 5
Contents......Page 9
Notation......Page 15
I Polynomial Interpolation......Page 19
II Limitations of Polynomial Approximation......Page 35
III Piecewise Linear Interpolation......Page 49
IV Piecewise Cubic Interpolation; CUBSPL......Page 57
V Best Approximation Properties of Complete Cubic Spline Interpolation and Its Error......Page 69
VI Parabolic Spline Interpolation......Page 77
VII A Representation for Piecewise Polynomial Functions; PPVALU, INTERV......Page 87
VIII The Spaces \Pi_{IX The Representation of PP Functions by B-Splines......Page 105
X The Stable Evaluation of B-Splines and Splines; BSPLVB, BVALUE, BSPLPP......Page 127
XI The B-Spline Series, Control Points, and Knot Insertion......Page 149
XII Local Spline Approximation and the Distance from Splines; NEWNOT......Page 163
XIII Spline Interpolation; SPLINT, SPLOPT......Page 189
XIV Smoothing and Least-Squares Approximation; SMOOTH, L2APPR......Page 225
XV The Numerical Solution of an Ordinary Differential Equation by Collocation; BSPLVD, COLLOC......Page 261
XVI Taut Splines, Periodic Splines, Cardinal Splines and the Approximation of Curves; TAUTSP......Page 281
XVII Surface Approximation by Tensor Products......Page 309
Postscript on Things Not Covered......Page 331
Fortran Programs......Page 333
Bibliography......Page 349
Index......Page 359
