# Simultaneous Approximation by Algebraic Polynomials

## Related Articles

- On Approximation Scheme Preserving Reducibility and Its Applications. Crescenzi, P. // Theory of Computing Systems;Jan/Feb2000, Vol. 33 Issue 1, p1
Describes the polynomial-time approximation scheme (PTAS) preserving reducibility and its applications. Definition of PTAS using the basic ingredients of an optimization problem; Approximability properties of optimization problems; Connections with parameterized complexity; Relations between...

- Weighted Polynomial Approximation in the Complex Plane. Pritsker, I.E.; Varga, R.S. // Constructive Approximation;1998, Vol. 14 Issue 4, p475
Given a pair (G, W) of an open bounded set G in the complex plane and a weight function W(z) which is analytic and different from zero in G, we consider the problem of the locally uniform approximation of any function f(z), which is analytic in G, by weighted polynomials of the form...

- Uniform Asymptotics for Second-Kind Ultraspherical Polynomials on the Unit Circle. Golinskii, L. // Constructive Approximation;1998, Vol. 14 Issue 4, p599
The object under consideration is the system of orthonormal polynomials of the second kind which corresponds to ultraspherical weight function on the unit circle. We obtain a uniform asymptotic representation for such polynomials in the closed unit disk as well as two-sided bounds on the unit...

- Polynomial Approximation and Graph-Coloring. Paschos, V. Th. // Computing;2003, Vol. 70 Issue 1, p41
Consider a graph G=(V,E) of order n. In the minimum graph-coloring problem we try to color V with as few colors as possible so that no two adjacent vertices receive the same color. This problem is among the first ones proved to be intractable, and hence, it is very unlikely that an optimal...

- A Sharper Estimate on the Betti Numbers of Sets Defined by Quadratic Inequalities. Saugata Basu; Michael Kettner // Discrete & Computational Geometry;Jun2008, Vol. 39 Issue 4, p734
- On the bounded version of Hilbert's tenth problem. Pollett, Chris // Archive for Mathematical Logic;Jul2003, Vol. 42 Issue 5, p469
The paper establishes lower bounds on the provability of D = NP and the MRDP theorem in weak fragments of arithmetic. The theory I[sup 5] E[sub l] is shown to be unable to prove D = NP. This non-provability result is used to show that I[sup 5] E[sub 1] cannot prove the MRDP theorem. On the other...

- Weighted Polynomial Approximation for Convex External Fields. Vilmos Totik // Constructive Approximation;Apr2000, Vol. 16 Issue 2, p261
It is proven that if Q is convex and w(x)= exp(-Q(x)) is the corresponding weight, then every continuous function that vanishes outside the support of the extremal measure associated with w can be uniformly approximated by weighted polynomials of the form w[sup n] P[sub n] . This solves a...

- Polynomial Approximation on Convex Subsets of R[sup n]. Brudnyi, Y. A.; Kalton, N. J. // Constructive Approximation;Apr2000, Vol. 16 Issue 2, p161
Let K be a closed bounded convex subset of R[sup n] ; then by a result of the first author, which extends a classical theorem of Whitney there is a constant w[sub m] (K) so that for every continuous function f on K there is a polynomial Ï† of degree at most m-1 so that. |f(x)-Ï†(x)|â‰¤...

- Approximating quadratic programming with bound and quadratic constraints. Ye, Yinyu // Mathematical Programming;1999, Vol. 84 Issue 2, p219
Abstract. We consider the problem of approximating the global maximum of a quadratic program (QP) subject to bound and (simple) quadratic constraints. Based on several early results, we show that a 4/7-approximate solution can be obtained in polynomial time.