Chebyshev Approximation by Exponentials on Finite Subsets

Chebyshev Approximation by Exponentials on Finite Subsets

This paper is concerned with Chebyshev approximation by exponentials on finite subsets. We take into account that varisolvency does not hold for exponentials in general. A bound for the derivatives of exponentials is established and convergence of the solutions for the discrete problems is proved in the topology of compact convergence on the open interval.

On approximation by exponentials

We consider an approximation of L 2 0; 1) functions by linear combinations of exponentials fexp(? ` t)g. Having derived explicitly by Fourier transform techniques an orthogonal basis of exponentials, we specialize the discussion to the choicè = q ` , ` = 0; 1; : : :, where q 2 (0; 1). In that case the underlying orthogonal functions possess a particularly appealing form and they obey interestin...

Approximation by Piecewise Exponentials *

A function is called an exponential if it is a linear combination of products of polynomials with pure exponentials. In this paper lower and upper bounds for families of spaces of piecewise exponentials are established. In particular, the exact Lp-approximation order (1 _< p _<) is found for a family {Sh}h>O of function spaces when each Sh is generated by an exponential box spline and its multi...

University of Cambridge on Approximation by Exponentials

On Reverse Chebyshev Approximation

We investigate the problem of determining the largest domain where given error bounds can be satissed by an approximation of a given continuous real valued real function using polynomials of several kinds. Since the the error bounds are xed and the domain is variable we call this problem reverse Chebyshev approximation.