Results 271 to 280 of about 11,753 (303)

Convex Approximation by Rational Functions

SIAM Journal on Mathematical Analysis, 1995
The first part of the paper is concerned with the convex approximation to \(| x |\) by rational functions on the interval \([- 1,1]\). By using \(H^ \infty\) quadrature the approximation order \(c_ 1 e^{- c_ 2 \sqrt n}\) is obtained, where \(n\) denotes the degree of the approximating rational function.
Donald J Newman
exaly   +3 more sources

Approximation of the function �x� by rational functions

Mathematical Notes, 1974
We consider the problem of the approximation of the function ¦x¦ by rational functions. We make more precise the best approximation estimate obtained by A. P. Bulanov. We prove that for arbitrary positive integral n $$R_n [|x|]< Ane^{ - \pi \sqrt n } ,$$ where ...
exaly   +2 more sources

Approximation by Rational Functions

Journal of the London Mathematical Society, 1977
This paper contains eight theorems on the rational approximation of \(e^{-x}\) . We cite one of them by way of an example: ''Let \(p(x)\) and \(q(x)\) be any polynomials of degress at most \(n-1\) where \(n\geq 2\). Then we have \[ \left\|e^{-x}-\frac{p(x)}{q(x)}\right\|_{l_{\infty}(N)}\geq\frac{(e-1)^ne^{-4n}2^{-7n}}{n(3+2\sqrt2)^{n-1}}.'', \] (\(N ...
Erdős, Paul, Newman, D. J., Reddy, A. R.   +2 more
openaire   +1 more source

Rational functional network for function approximation

2008 3rd International Conference on Intelligent System and Knowledge Engineering, 2008
This paper presents a new functional network which is based on rational function. A learning algorithm of rational functional network is proposed, the learning of functional network parameters use Lagrange multipliers by means of auxiliary function and solving a system of linear equations obtain parameters.
Yongquan Zhou, Bai Liu, Zhucheng Xie, Dexiang Luo   +3 more
openaire   +1 more source

ON RATIONAL APPROXIMATION OF ANALYTIC FUNCTIONS

Mathematics of the USSR-Sbornik, 1973
Let E be a regular compact set, and D an arbitrary domain containing E. A constructive characterization is given of the class of functions analytic in D, using best approximation on E by rational functions with a specially chosen sequence of poles. Bibliography: 4 items.
openaire   +2 more sources

Matrix Padé Approximation of rational functions

Numerical Algorithms, 1997
This paper on rectangular matrix valued Padé approximation discusses existence and uniqueness issues of left and right approximants as well as certain minimality conditions on the degrees in numerator and denominator matrix polynomials of the approximants.
Celina Pestano-Gabino, Concepción González-Concepción   +1 more
openaire   +1 more source

Best approximations by rational functions

Mathematical Notes of the Academy of Sciences of the USSR, 1971
Description of a general class of real continuous functions cn a segment Δ of the real line for which a best rational approximation with complex coefficients is not unique.
openaire   +3 more sources

The Rational Approximation of Real Functions

American Journal of Mathematics, 1978
Publisher Summary This chapter discusses the rational approximation of real functions. The chapter is closely related to the classical theory of best uniform approximation of continuous functions by quotients of polynomials. The chapter illustrates that if the function being approximated is the real function f, then its best approximation in P n ( ℭ
openaire   +2 more sources

RATIONAL APPROXIMATION OF ANALYTIC FUNCTIONS

Russian Academy of Sciences. Sbornik Mathematics, 1994
Let \(E\) be an arbitrary compact set in the extended complex plane \(\overline \mathbb{C}\), \(f\) analytic on \(E\), and for any nonnegative integer \(n\) let \(\rho_ n\) denote the uniformly best error of the rational approximation of \(f\) on \(E\), i.e.
openaire   +2 more sources