Results 231 to 240 of about 19,451 (267)

Approximation of Irrationals By Rationals

The Mathematical Gazette, 1964
Professor Forder’s elegantly simple method in Note 3068 (Math. Gazette 47 (1963), 237-8) can be extended to prove a more general result. Let k be any positive integer, ξ any irrational number, a
openaire   +1 more source

On Rational Approximations of Semigroups

SIAM Journal on Numerical Analysis, 1979
We show that if $r^n (hA),nh = t$, is an A-acceptable rational approximation of a strongly continuous semigroup $e^{tA} $ on a Banach space, then for t bounded, $\| {r^n (hA)} \| \leqq Cn^{{1/2}} $, with certain improvements under additional hypotheses on r.
Brenner, Philip, Thomee, Vidar
openaire   +1 more source

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

On the Approximation of Irrationals by Rationals

Mathematische Nachrichten, 1998
AbstractLet ξ be a real irrational number, anda≧ 0,b≧ 0,s> 1 be integers. A theorem of S. UCHIYAMA states that there are infinitely many pairs of integersuand v ≠ 0 such that OVBARξ−u/vOVBAR ≤s2/4v2andua,vbmods, provided that it is not a  6  0 mod s. It is shown that this result is best‐possible for all integerss> 1.
openaire   +2 more sources

Uniform rational approximation

Proceedings of the American Mathematical Society, 1995
Let K be a compact subset of the complex plane C \mathbb {C}
openaire   +2 more sources

An Interpolatory Rational Approximation

Canadian Mathematical Bulletin, 1978
The classical Hermite-Fejér interpolation process is a positive linear mapping from C[-1, 1] into the space of polynomials of degree ≤2n-1. If Tn(x) denotes the Tchebisheff polynomial of degree n and xk = xnk(k = 1,2, …, n) its roots, then for any given f∈ C[-1, 1] the Hermite-Fejér image Hnf of f is defined by1 ...
openaire   +1 more source

On Rational Number Reconstruction and Approximation

SIAM Journal on Computing, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Victor Y. Pan, Xinmao Wang
openaire   +2 more sources

Rational approximations to \(\pi\)

1971
Using an IBM 1130 computer, we have generated the first 20, 000 partial quotients in the ordinary continued fraction representation of pie. © 1971 American Mathematical Society.
Choong, K.Y., Daykin, D.E., Rathbone, C.R.   +2 more
openaire   +2 more sources

RATIONAL APPROXIMATION AND PLURIPOLAR SETS

Mathematics of the USSR-Sbornik, 1984
The main result in the article isTheorem. Let be a closed set such that and is a pseudoconvex domain. If for almost every complex line passing through 0 the intersection is polar in , then is a pluripolar set in .This theorem is then applied to the analysis of sets of singularities of holomorphic functions which are rapidly approximated by rational ...
openaire   +2 more sources

RATIONAL APPROXIMATIONS TO ALGEBRAIC NUMBERS

Mathematics of the USSR-Izvestiya, 1971
In this article we derive a new effective estimate of rational approximations to algebraic numbers simultaneously in an Archimedian and several non-Archimedian metrics.
openaire   +2 more sources