Constructive Approximation

Ronald A. DeVore, George G. Lorentz (Autoren)

Buch | Softcover

X, 452 Seiten

2010 | 1. Softcover reprint of hardcover 1st ed. 1993
Springer Berlin (Verlag)
978-3-642-08075-3 (ISBN)

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The present book deals with some basic problems of Approximation Theory: with properties of polynomials and splines, with approximation by poly- mials, splines, linear operators. It also provides the necessary material ab out different function spaces. In some sense, this is a modern version of the corre sponding parts of the book of one of us (Lorentz [A-1966]). We have tried to give a complete exposition of the main, basic theorems of the theory, without going into too much detail, treating the most general cases or discussing very special problems. There are essential limitations: this is a book about approximation of functions of one real variable. But Approxima tion Theory of functions of several real or of complex variables would require new books. Very little is given on interpolation. But even with these restric tions, proofs of some deep and important results, like Korneichuk's theorems about approximation in Lipschitz spaces, could not be included. Another book, with different authors, "Constructive Approximation, Advanced Problems", is in preparation. There is an extensive bibliography, which can be used also as an Author Index: each paper is supplied with references for the page or pages where it has been used.

The book describes function spaces used in approximation, the needed functional analytic tools. It develops basic properties of polynomials, splines, linear operators that are used for approximation (and interpolation). The book takes the reader up to and into the recent great advances of Approximation Theory and emphasizes good proofs, logical selection of material, avoidance of superfluous details.

1. Theorems of Weierstrass.- 2. Spaces of Functions.- 3. Best Approximation.- 4. Properties of Polynomials.- 5. Splines.- 6. K-Functionals and Interpolation Spaces.- 7. Central Theorems of Approximation.- 8. Influence of Endpoints in Polynomial Approximation.- 9. Approximation by Operators.- 10. Bernstein Polynomials.- 11. Approximation of Classes of Functions, Müntz Theorems.- 12. Spline Approximation.- 13. Spline Interpolation and Projections onto Spline Spaces.

"This is a stimulating book and a mine of useful techniques and results..." Bulletin of the LMS

Erscheint lt. Verlag	1.12.2010
Reihe/Serie	Grundlehren der mathematischen Wissenschaften
Zusatzinfo	X, 452 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	686 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	algorithms • Approximation Theory • CON_D043 • Interpolation • operators • Splines
ISBN-10	3-642-08075-8 / 3642080758
ISBN-13	978-3-642-08075-3 / 9783642080753
Zustand	Neuware