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Approximation Theory and Methods

Approximation Theory and Methods - 81 edition

ISBN13: 978-0521295147

Cover of Approximation Theory and Methods 81 (ISBN 978-0521295147)
ISBN13: 978-0521295147
ISBN10: 0521295149
Edition: 81
Copyright: 1981
Publisher: Cambridge University Press
Published: 1981
International: No

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Approximation Theory and Methods - 81 edition

ISBN13: 978-0521295147

M. J. Powell

ISBN13: 978-0521295147
ISBN10: 0521295149
Edition: 81
Copyright: 1981
Publisher: Cambridge University Press
Published: 1981
International: No
Summary

Preface; 1. The approximation problem and existence of best approximations; 2. The uniqueness of best approximations; 3. Approximation operators and some approximating functions; 4. Polynomial interpolation; 5. Divided differences; 6. The uniform convergence of polynomial approximations; 7. The theory of minimax approximation; 8. The exchange algorithm; 9. The convergence of the exchange algorithm; 10. Rational approximation by the exchange algorithm; 11. Least squares approximation; 12. Properties of orthogonal polynomials; 13. Approximation of periodic functions; 14. The theory of best L1 approximation; 15. An example of L1 approximation and the discrete case; 16. The order of convergence of polynomial approximations; 17. The uniform boundedness theorem; 18. Interpolation by piecewise polynomials; 19. B-splines; 20. Convergence properties of spline approximations; 21. Knot positions and the calculation of spline approximations; 22. The Peano kernel theorem; 23. Natural and perfect splines; 24. Optimal interpolation; Appendices; Index.

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