Quasi Interpolation 1st Edition by Martin Buhmann, Janin Jäger ISBN 9781107072633 1107072638

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Product details:

ISBN 10: 1107072638
ISBN 13: 9781107072633
Author: Martin Buhmann, Janin Jäger

Quasi Interpolation 1st Edition Table of contents:

1 Introduction

2 Generalities on Quasi-Interpolation

2.1 Approximation Properties

2.2 Main Examples of Quasi-Interpolants

2.3 Some Applications Connected with Different Forms of Quasi-Interpolants

3 Univariate RBF Quasi-Interpolants

3.1 Univariate Quasi-Interpolants

3.2 Examples of Convergence Results

3.3 Further Examples

3.4 Notes

4 Spline Quasi-Interpolants

4.1 Spaces of Piecewise Polynomials

4.2 General Form of Spline Quasi-Interpolants

4.3 Marsden’s Identity and de Boor–Fix Differential Quasi-Interpolants

4.4 Approximation Order and Error Estimates

4.5 Discrete Quasi-Interpolants

4.6 Integral Quasi-Interpolants

4.7 Local Spline Projectors

4.8 Near-Minimally Normed Quasi-Interpolants

4.9 Schoenberg’s Quasi-Interpolation and Discrete Spline Quasi-Interpolants with Uniform Partition

4.10 Notes

5 Quasi-Interpolants for Periodic Functions

5.1 Trigonometric Spline Quasi-interpolants

5.2 Multiquadric Trigonometric Spline Quasi-Interpolants

5.3 De la Vallée Poussin Quasi-Interpolants

5.4 Notes

6 Multivariate Spline Quasi-Interpolants

6.1 Quasi-Interpolants from Tensor Product Splines

6.2 Spline Spaces Constructed from Shifts of One Spline

6.3 Notes

7 Multivariate Quasi-Interpolants: Construction in n Dimensions

7.1 Introduction and Further Notation

7.2 Polynomial Reproduction

7.3 Examples

7.4 Convergence Theorems

7.5 Quasi-Interpolation via Approximate Approximation

7.6 Notes

8 Quasi-Interpolation on the Sphere

8.1 Spherical Quasi-Interpolation using Tensor Products

8.2 Quasi-Interpolation on the Sphere Using Approximate Fourier Coefficients

8.3 Quasi-Interpolants using Shepard’s Method for the Sphere

8.4 Notes

9 Other Quasi-Interpolants and Wavelets

9.1 Prewavelets with Radial Basis Functions and Quasi-Lagrange Bases

9.2 Least-Squares Approximations as Quasi-Interpolants

9.3 Weierstrass Operators

9.4 Notes

10 Special Cases and Applications

10.1 Even- and Odd-Dimensional Spaces and Equally Spaced Centres

10.2 A Look at the Inverse Multiquadric Radial Function in One Dimension

10.3 Applications: Fredholm Integral Equations

10.4 Applications: Numerical Solution of Partial Differential Equations

10.5 Compression in the Space of Continuous Functions

10.6 Notes

References

Index

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Tags: Martin Buhmann, Janin Jäger, Quasi Interpolation