| Constructive Approximation 1993 Edition Contributor(s): DeVore, Ronald A. (Author), Lorentz, George G. (Author) |
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ISBN: 3540506276 ISBN-13: 9783540506270 Publisher: Springer OUR PRICE: $151.99 Product Type: Hardcover - Other Formats Published: November 1993 Annotation: The purpose of this book and its sequel is to give a connected, unified exposition of Approximation Theory for functions of one real variable. Great care has been taken to provide reliable and good proofs, and to establish a logical selection of material, with emphasis on principal results. The history of the subject is not neglected. Methods of functional analysis are used when necessary, as are complex variable methods for real problems. Practical algorithms of approximation are included. Important old results are not missing, but at least half of the material has never yet appeared in books. The first book describes spaces of functions: Sobolev, Lipschitz, Besov rearrangement-invariant function spaces, interpolation of operators. Then we have Weierstrass and best approximation theorems, properties of polynomials and of splines: inequalities, interpolation (also Birkhoff), zero properties. Approximation by operators treats positive operators, projections, also those of minimal norm, saturation phenomena, a modern theory of Bernstein polynomials. Chapters on splines deal with the selection of knots, splines with equidistant, dyadic, fixed and free knots, with identification of approximation spaces, further with orthogonal projections onto splines, cardinal splines, shape preserving algorithms. With no equally comprehensive and up-to-date competitor in the available literature, these two volumes will be a welcome reference for a wide audience of mathematicians and engineers. They can be used as the basis for courses, or as a means to enter research in the subject. |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Number Systems - Mathematics | Functional Analysis |
| Dewey: 511.42 |
| LCCN: 93018420 |
| Series: Grundlehren Der Mathematischen Wissenschaften (Springer Hardcover) |
| Physical Information: 1" H x 6.14" W x 9.21" (1.82 lbs) 452 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |