Marta García-Esnaola

Error bounds for linear complementarity problems for B-matrices

A square real matrix with positive row sums is a B-matrix if all its off-diagonal elements are bounded above by the corresponding row means. We give error bounds for the linear complementarity problem when the matrix involved is a B-matrix. Perturbation bounds for B-matrix linear complementarity problems are also considered. The sharpness of the bounds is shown.

Error bounds for linear complementarity problems involving B S -matrices

Abstract The class of B S -matrices is a subclass of the P -matrices containing B -matrices. Error bounds for the linear complementarity problem when the matrix involved is a B S -matrix are presented. Perturbation bounds of B S -matrix linear complementarity problems are also considered. The sharpness of the bounds with respect to other bounds is shown.

Convexity of rational curves and total positivity

We analyze convexity preserving properties of curves from a geometric point of view. We also characterize totally positive systems of functions in terms of geometric convexity preserving properties of the rational curves. Rational Bezier and nonuniform rational B-spline curves are included in this setting.

Error bounds for linear complementarity problems of Nekrasov matrices

We present error bounds for the linear complementarity problem when the involved matrix is a Nekrasov matrix and also when it is a Σ

B-Nekrasov matrices and error bounds for linear complementarity problems

\Sigma

Lagrange interpolation on conics and cubics

-Nekrasov matrix. The new bounds can improve considerably other previous bounds.

Sign consistent linear programming problems

The class of B-Nekrasov matrices is a subclass of P-matrices that contains Nekrasov Z-matrices with positive diagonal entries as well as B-matrices. Error bounds for the linear complementarity problem when the involved matrix is a B-Nekrasov matrix are presented. Numerical examples show the sharpness and applicability of the bounds.

Global convexity of curves and polygons

A bivariate polynomial interpolation problem for points lying on an algebraic curve is introduced. The geometric characterization introduced by Chung and Yao, which provides simple Lagrange formulae, is here analyzed for interpolation points lying on a line, a conic or a cubic.

On the asymptotic optimality of error bounds for some linear complementarity problems

This article studies linear programming problems in which all minors of maximal order of the coefficient matrix have the same sign. We analyse the relationship between a special structure of the non-degenerate dual feasible bases of a linear programming problem and the structure of its associated matrix. In the particular case in which the matrix has all minors of each order k with the same strict sign ϵ k , we provide a dual simplex revised method with good stability properties. In particular, this method can be applied to the totally positive linear programming problems, of great interest in many applications.

A comparison of error bounds for linear complementarity problems of H-matrices☆

In this paper we consider a definition of convexity given by Schoenberg and show the connection with other definitions of convexity used by several authors. The representations of curves which preserve the convexity of the control polygon are analyzed and described.