A Simple Rule to find a Basic Feasible Solution

This short note provides and proves an easy algorithm to find a basic feasible solution for the Simplex Algorithm. The method uses a rule similar to Bland’s rule for the initial phase of the algorithm

On the Real CF-Method for Polynomial Approximation and Strong Unicity Constants

AbstractWe consider uniform polynomial approximation on [ −1, 1]. For the class of functions which are analytic in an ellipse with foci ± 1 and sum of semiaxes greater than 8.1722…, we prove several asymptotic results on the best approximation. We describe the CF-approximation method and prove that, for our class of functions, the CF-approximation is “not far away” from the best one. With the help of this result we show a Kadec type result on the alternants and prove a conjecture of Poreda on the strong uniqueness constants. Also we prove a lemma on the distance between the best approximation and a “good” approximating polynomial

On the Zeros of Sequences of Polynomials

AbstractIn this paper we generalize a result of Blatt, Saff, and Simkani on the limit distribution of zeros of sequences of polynomials. In a typical application these polynomials converge on a compact subset E of the complex plane. The highest coefficient of the polynomials plays an important role in the theorem of Blatt, Saff, and Simkani. In this paper we replace the behavior of the highest coefficient by the behavior of the sequence on some compact set in C\E. Furthermore we show how this generalization can be applied to sequences of maximally convergent polynomials