The first investigations of nonlinear approximation problems were
made by P.L. Chebyshev in the last century, and the entire theory
of uniform approxima tion is strongly connected with his name. By
making use of his ideas, the theories of best uniform approximation
by rational functions and by polynomials were developed over the
years in an almost unified framework. The difference between linear
and rational approximation and its implications first became
apparent in the 1960's. At roughly the same time other approaches
to nonlinear approximation were also developed. The use of new
tools, such as nonlinear functional analysis and topological
methods, showed that linearization is not sufficient for a complete
treatment of nonlinear families. In particular, the application of
global analysis and the consideration of flows on the family of
approximating functions intro duced ideas which were previously
unknown in approximation theory. These were and still are important
in many branches of analysis. On the other hand, methods developed
for nonlinear approximation prob lems can often be successfully
applied to problems which belong to or arise from linear
approximation. An important example is the solution of moment
problems via rational approximation. Best quadrature formulae or
the search for best linear spaces often leads to the consideration
of spline functions with free nodes. The most famous problem of
this kind, namely best interpolation by poly nomials, is treated in
the appendix of this book."
General
| Imprint: |
Springer-Verlag
|
| Country of origin: |
Germany |
| Series: |
Springer Series in Computational Mathematics, 7 |
| Release date: |
October 2011 |
| First published: |
1986 |
| Authors: |
Dietrich Braess
|
| Dimensions: |
235 x 155 x 16mm (L x W x T) |
| Format: |
Paperback
|
| Pages: |
290 |
| Edition: |
Softcover reprint of the original 1st ed. 1986 |
| ISBN-13: |
978-3-642-64883-0 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Numerical analysis
Promotions
|
| LSN: |
3-642-64883-5 |
| Barcode: |
9783642648830 |
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