In this paper we present a graph grammar based direct solver algorithm for hp-adaptive finite element method simulations with point singularities. The solver algorithm is obtained by representing computational mesh as a graph and prescribing the solver algorithm by graph grammar productions. Classical direct solvers deliver O(Np+N) computational cost for regular 2D grids, and O(Np+N) for regula...

Here we are concerned with the best approximation by polynomials to rational functions in the uniform norm. We give some new theorems about the best approximation of 1/(1 + x) and 1/(x − a) where a > 1. Finally we extend this problem to that of computing the best approximation of the Chebyshev expansion in uniform norm and give some results and conjectures about this.  2005 IMACS. Published by...

Let X denote a compact set in the complex plane ℂ and zn≔{zn,j}j=0n be family of points that lie on X. Then norm ‖Azn‖ operator Azn maps Banach space C(X) to Πn polynomials degree ≤n, defined by Aznf=pn, where pn∈Πn is polynomial interpolates f∈C(X) at zn, called Lebesgue constant zn. While bulk this paper study Lagrange interpolation Fejér zn∗≔{zn,j∗}j=0n, their proper adjustment, an open arc ...

In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.

in this paper, we propose a parametric uniform approximation method to solve np-hard absolute value equations. for this, we uniformly approximate absolute value in such a way that the nonsmooth absolute value equation can be formulated as a smooth nonlinear equation. by solving the parametric smooth nonlinear equation using newton method, for a decreasing sequence of parameters, we can get the ...

In 1877, E. I. Zolotarev [19, 2] found an explicit expression, in terms of elliptic functions, of the rational function of given degree m which is uniformly closest to sgn (x) on the union of two intervals [−1,−a] ∪ [a, 1]. This result was subject to many generalizations, and it has applications in electric engineering. Surprisingly, to the best of our knowledge, the similar problem for polynom...

Abstract. The classical Gibbs phenomenon for the Fourier sections (best L2trigonometric polynomial approximants) of a jump function asserts that, near the jump, the~e sections "overshoot" the function by an asymptotically constant factor g (the L2-Gibbs constant). In this paper we show that, for a class of one-jump discontinuous functions, a similar phenomenon holds for the trigonometric polyno...