Results 221 to 230 of about 429,249 (270)

Multivariate simultaneous approximation

Constructive Approximation, 2002
Using convolution techniques, the Fourier transform, and complex analysis, theorems of Jackson type are given, for the simultaneous approximation of a function of class \(C^m\) and its partial derivatives, by a polynomial and the corresponding partial derivatives.
BAGBY T., BOS, LEONARD PETER, LEVENBERG L.   +2 more
openaire   +3 more sources

Simultaneous Polynomial Approximation

SIAM Journal on Mathematical Analysis, 1993
The authors prove the approximation theorem on simultaneous approximation of \(f\in C^ s[- 1,1]\) and its derivatives of order \(j\), \(0\leq j\leq s\), by polynomials of degree \(n\) and their derivatives which has filled the gap between Timan-Trigub's type theorem and the classical norm estimate of the Jackson type.
Ditzian, Z., Jiang, Dechang, Leviatan, D.   +2 more
openaire   +2 more sources

Simultaneous Diophantine Approximation

Proceedings of the London Mathematical Society, 1952
Proof of the theorem: ``Let \(c > 46^{-1/4}\). Then, for every pair of real irrational numbers \(\alpha, \beta\), there exist infinitely many solutions \(p, q, r > 0\) of \(r(p-\alpha r)^2 < c\), \(r(q- \beta r)^2 < c\) in integers.'' This result slightly improves one by \textit{P. Mullender} [Ann. Math. (2) 52, 417-426 (1950; Zbl 0037.17102)].
openaire   +2 more sources

Simultaneous Diophantine Approximation

Canadian Journal of Mathematics, 1950
Summary of results. The principal result of this paper is as follows: given any set of real numbers z1, z2, & , zn and an integer t we can find an integer and a set of integers p1, p2 & , pn such that(0.11).Also, if n = 2, we can, given t, produce numbers z1 and z2 such that(0.12)This supersedes the results of Nils Pipping (Acta Aboensis, vol.
openaire   +3 more sources

Suitable Norms for Simultaneous Approximation

Acta Mathematica Hungarica, 1997
The most common way to study simultaneous approximation of two points \(x,y\) of a normed linear space \(E\) from a subset \(M\) of \(E\), is to consider a suitable norm in \(E\times E\) (for instance, \(\| (u,v)\| =\sup(\| u\| ,\| v\|)\), \(\| (u,v)\| =\| u\| +\| v\|)\) and to reduce this problem to the ordinary approximation of the single point \((x ...
Benítez, Carlos, Fernández, Manuel, Soriano, María L.   +2 more
openaire   +3 more sources

On simultaneous approximation

Numerical Functional Analysis and Optimization, 1998
In this exposition, we investigate in an extended framework the problem of simultaneous best approximation. Refinement of a formula for the subdifferential of restricted radius of a p-bounded set leads us to explore some interesting results on strong uniqueness of simultaneous best approximants. In particular, we also.
LAURENT, PJ, PAI, D
openaire   +2 more sources

Simultaneous asymptotic Diophantine approximations

Mathematika, 1967
Let θ 1 , …, θ k be k real numbers. Suppose ψ( t ) is a positive decreasing function of the positive variable t . Define λ( N ), for all positive integers N , to be the number of solutions in integers p 1 …, p k , q of the inequalities ...
openaire   +2 more sources

ON SIMULTANEOUS PADÉ APPROXIMANTS

Mathematics of the USSR-Sbornik, 1982
A rather large class of systems of functions is investigated in connection with the simultaneous Pade approximants (normality, perfectness, problems of uniform convergence).Bibliography: 20 titles.
openaire   +2 more sources

Simultaneous Approximation and Algebraic Independence

The Ramanujan Journal, 1997
Rappelons la notion de mesure d'approximation simultanée (MAS): soit \(\theta= (\theta_1,\dots,\theta_n)\in \mathbb{C}^n\); une application \(\varphi: \mathbb{N}\times [0,+\infty[\to [0,+\infty]\) est une MAS pour \(\theta\) si il existe \(D_0\in\mathbb{N}\) et \(h_0\geq 1\) tels que, pour tout entier \(D\geq D_0\), tout nombre réel \(h\geq h_0\) et ...
Roy, Damien, Waldschmidt, Michel
openaire   +2 more sources