| Preface Notation Ⅰ Polynomial 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 Ⅱ Limitations 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 Ⅲ Piecewise Linear Approximation Broken line interpolation Broken line interpolation is nearly optimal Least．squares approximation by broken lines Good meshes Problems Ⅲ Piecewise 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 Ⅵ Parabolic Spline Interpolation Ⅶ A Representation for Piecewise Polynomial Functions Piecewise polynomial functions The subroutine PPVALU The subroutine INTERV Problems Ⅷ The 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 Ⅸ The Representation of PP Functions by B-Splines Ⅹ The Stable Evaluation of B-Splines and Splines Ⅺ THe B-Spline Series，Control Points，and Knot Insertion Ⅻ Local Spline Approximation and the Distance from Splines ⅩⅢ Spline Interpolation ⅩⅣ Smoothing 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 |
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