In this article, we present a simple direct matrix method for analytically computing the Jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integrodifferential equations. This method is based on a formulation of the discretized equations in vector form using only matrix-vector products and component-wise operations. By applying simple matrixbased different...

This is an overview of the life and scientific legacy of Leonid V. Kantorovich (1912--1986) who stood at the cradle of linear programming, vector lattices, and computational mathematics. Linear programming as well as mathematical economics belongs to or at least borders the realm of applied mathematics. The epithets “pure” and “applied” for mathematics have many deficiencies provoking endless d...

The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovich inequalities for positive real numbers. We also prove a generalization of Fiedler’s inequality.

In this pedagogical article, we present a simple direct matrix method for analytically computing the Jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integro-differential equations. The method is based on a formulation of the discretized equations in vector form using only matrix-vector products and componentwise operations. By applying simple matrix-bas...