A Practical Guide to Splines (Applied Mathematical Sciences v. 27 1st ed. 1978. 1st hardcover printing 2001)
By: Carl De Boor (author)Paperback
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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.
Preface.- Notation.- Table of Contents.- I Polynomial Interpolation.- II Limitations of Polynomial Approximation.- III Piecewise Linear Approximation.- IV Piecewise Cubic Interpolation; CUBSPL.- V Best Approximation Properties of Complete Cubic Spline Interpolation and its Error.- VI Parabolic Spline Interpolation.- VII A Representation for Piecewise Polynomial Functions; PPVALU, INTERV.- VIII The Spaces PkE,v and the Truncated Power Basis.- IX The Representation of PP Functions by B-splines.- X The Stable Evaluation of B-splines and Splines; BSPLVB, BVALUE, BSPLPP.- XI The B-Spline Series.- XII Local Spline Approximation Methods and the Distance from Splines; NEWNOT.- XIII Spline Interpolation; SPLINT, SPLOPT.- XIV Smoothing and Least-Square Approximation; SMOOTH, L2APPR.- XV The Numerical Solution of an Ordinary Differential Equation by Collocation; BSPLVD, COLLOC.- XVI Taut Splines, Periodic Splines, Cardinal Splines and the Approximation of Curves; TAUTSP.- XVII Surface Approximation by Tensor Products.- Postscript on Things not Covered.- Appendix.- Listing of SOLVEBLOK Package.- List of Fortran Programs.- Bibliography.- Subject Index.
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- ID: 9780387953663
1st ed. 1978. 1st hardcover printing 2001
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