Nonlinear Numerical Methods And Rational Approximation
Download Nonlinear Numerical Methods And Rational Approximation PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Nonlinear Numerical Methods And Rational Approximation book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Nonlinear Approximation Theory
Author: Dietrich Braess
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
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 branchesof 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.
Nonlinear Numerical Methods and Rational Approximation
Author: A. Cuyt
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; use Stein spaces. And in addition to this there are and prediction and electrical engineering can such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Nonlinear Numerical Methods and Rational Approximation II
These are the proceedings of the international conference on Nonlinear Numerical Methods and Rational Approximation II, which Dr. Cuyt organized at the University of Antwerp, Belgium, 5--11 September 1992. The conference focused on the use of rational functions in different fields of numerical analysis. The invited speakers discussed five main topics, which are represented by the five sections of this book: orthogonal polynomials, rational interpolation, rational approximation, Pade approximation and continued fractions. Multivariate and multidimensional problems, application and implementations of each main topic are also considered. For specialists in the field of nonlinear numerical methods and rational approximation.