and Applied Analysis 3 Algorithm 2.1 consider interchange a basic variable xB,p and nonbasic variable xN,j . aql ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩ 1 apj , q p, l j apl apj , q p, l / j −qj apj , q / p, l j aql − aplaqj apj , q / p, l / j , b1 l ⎧ ⎪ ⎪⎨

The teaching experience of the revised simplex method in matrix notation on the blackboard leads us to prepare a visualization alternative, useful for the constituting part of the education liturgy. According to our approach the educator does not spend anymore valuable time on boring calculations while the student understands complex mathematical concepts. Our courseware has unique features lik...

An active area of research for linear programming is to construct initial Simplex tableau that is close to the optimal solution, and to improve its pivoting selection strategies efficiently. In this paper, we present a new approach to the problem of initialization and pivoting rules: the algorithm is free from any artificial variables and artificial constraints, known as the big-M methods. By s...

GRADIENT ION CHROMATOGRAPHY WAS USED FOR THE SEPARATION OF EIGHT SUGARS: arabitol, cellobiose, fructose, fucose, lactulose, melibiose, N-acetyl-D-glucosamine, and raffinose. The separation method was optimized using a combination of simplex or genetic algorithm with the isocratic-to-gradient retention modeling. Both the simplex and genetic algorithms provided well separated chromatograms in a s...

This paper deals with the roundingerror analysis of the simplex method for solving linear-programming problems. We prove that in general any simplex-type algorithm is not well behaved, which means that the computed solution cannot be considered as an exact solution to a slightly perturbed problem. We also point out that simplex algorithms with well-behaved updating techniques (such as the Barte...

We investigate the problem of finding the first basic solution in the simplex algorithm. A modification of two phases simplex method is presented and its implementation in programming language Visual Basic is described. A few Netlib examples are presented.

We propose a methodology for animating complexmodels based on simplexmesh represen tation and deformation A simplex mesh is characterized by a connectivity between vertices of three and can be obtained by duality from a triangulation In addition to their generality of representation simplex meshes have a compact and unambiguous shape description related to the notion of mean curvature We devise...

Recent work in mathematical neuroscience has calculated the directed graph homology of simplicial complex given by brains sparse adjacency graph, so called connectome. These biological connectomes show an abundance both high-dimensional simplices and Betti-numbers all viable dimensions - contrast to Erd\H{o}s-R\'enyi-graphs comparable size density. An analysis synthetically trained reveals simi...

Block motion estimation can be regarded as a function minimization problem in a finite-dimensional space. Therefore, fast block motion estimation can be achieved by using an efficient function minimization algorithm instead of a predefined search pattern, such as diamond search. Downhill simplex search is an efficient derivative-free function minimization algorithm. In this paper, we proposed a...