A Practical Guide to Splines样条实用指南
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作者： Carl De Boor著
出 版 社：
出版时间： 2001-11-1字数：版次： 1页数： 346印刷时间： 2001/11/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387953663包装： 精装内容简介
This book is based on the author's 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 VII and VIII，while chapters IX，X，and XI are devoted to B-splines。The distances from splines with fixed and with variable knots is discussed in chapter XII。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。The present text version differs from the original in several respects。The book is now typeset （in plain TeX）， the Fortran programs now make use of Fortran 77 features。he figures have been redrawn with the aid of Matlab，various errors have been corrected，and many more formal statements have been provided with proofs。Further，all formal statements and equations have been numbered by the same numbering system，to make it easier to find any particular item。A major change has occured in Chapters IX-XI where the B-spline theory is now developed directly from the recurrence relations without recourse to divided differences。This has brought in knot insertion as a powerful tool for providing simple proofs concerning the shape-preserving properties of the B-spline series。
目录
Preface
Notation
ⅠPolynomial Interpolation
Polynomial interpolation：Lagrange form
Polynomial Interpolation：Divided differences and Newton form
Divided difierence table
Example：Osculatory interpolation to the logarithm
Evaluation of the Newton form
Example：Computing the derivatives of
Other polynomial forms and conditions
Problems
a polynomial in Newton form 1
ⅡLimitations of Polynomial Approximation
Uniform spacing of data Call have bad consequences
Chebyshev sites are good
Runge example with Chebyshev sites
Squareroot example
Interpolation at Chebyshev sites is nearly optimal
The distance from polynomials
Problems
ⅢPiecewise Linear Approximation
Broken line interpolation
Broken line interpolation is nearly optimal
Least．squares approximation by broken lines
Good meshes
Problems
ⅢPiecewise Cubic Interpolation
Piecewise cubic Hermite interpolation
Runge example continued
Piecewise cubic Bessel interpolation
Akima’S interpolation
Cubic spline interpolation
Boundary conditions
Problems
ⅤBest Approximation Properties of Complete Cubic Spline
Interpolation and Its Error
Problems
Problems
ⅥParabolic Spline Interpolation
ⅦA Representation for Piecewise Polynomial Functions
Piecewise polynomial functions
The subroutine PPVALU
The subroutine INTERV
Problems
ⅧThe Spaces and the Truncated Power Basis
Example；The smoothing of a histogram by parabolic splines
The space Ⅱ
Tile truncated power basis for Ⅱand Ⅱ
Example：The truncated power basis can be bad
Problems
ⅨThe Representation of PP Functions by B-Splines
ⅩThe Stable Evaluation of B-Splines and Splines
ⅪTHe B-Spline Series，Control Points，and Knot Insertion
ⅫLocal Spline Approximation and the Distance from Splines
ⅩⅢSpline Interpolation
ⅩⅣSmoothing and Least-Square Approximation
ⅩⅤ The Numerical Solution of an Ordinary Differential Equation by Collocation
ⅩⅥ Taut Splines, Periodic Splines, Cardinal Splines and the Approximation of Curves
ⅩⅦ Surface Approximation by Tensor Products.
Postscript on Things not Covered
Appendix
Bibliography
Index
