Polynomial operators for spectral approximation of piecewise analytic functions
نویسندگان
چکیده
منابع مشابه
Polynomial operators for spectral approximation of piecewise analytic functions
We construct a sequence of globally defined polynomial valued operators, using linear combinations of either the coefficients in the orthogonal polynomial expansion of the target function with respect to a very general mass distribution μ or the values of the function at suitable points on [−1, 1], so that the degree of approximation by these operators globally is commensurate with the degree o...
متن کاملThe approximation of piecewise linear membership functions and lukasiewicz operators
In this paper we propose an approximation of piecewise linear membership functions with the help of sigmoid functions and certain arithmetic operations. The gradient-based tuning of piecewise linear membership functions can be achieved with the proposed efficient approximation because it has simple continuous derivatives. With this construction we can even approximate the Łukasiewicz operator f...
متن کاملAnalytic approximation of transmutation operators and related systems of functions
In [27] a method for approximate solution of Sturm-Liouville equations and related spectral problems was presented based on the construction of the Delsarte transmutation operators. The problem of numerical approximation of solutions and eigendata was reduced to approximation of a primitive of the potential by a finite linear combination of certain specially constructed functions obtained from ...
متن کاملRemarks on Piecewise Polynomial Approximation
The theoretical and experimental background for the approximation of "real-world" functions is reviewed to motivate the use of piecewise polynomial approximations. It is possible in practice ~o achieve the results suggested by the theory for piecewise polynomials. A convergent adaptive algorithm is outlined which effectively and efficiently computes smooth piecewise polynomial approxImations to...
متن کاملSpectral Approximation for Compact Operators
In this paper a general spectral approximation theory is developed for compact operators on a Banach space. Results are obtained on the approximation of eigenvalues and generalized eigenvectors. These results are applied in a variety of situations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2009
ISSN: 1063-5203
DOI: 10.1016/j.acha.2008.03.002