The solution of linear interval equations by a linear programming method

Sparse nonnegative solution of underdetermined linear equations by linear programming.

Consider an underdetermined system of linear equations y = Ax with known y and d x n matrix A. We seek the nonnegative x with the fewest nonzeros satisfying y = Ax. In general, this problem is NP-hard. However, for many matrices A there is a threshold phenomenon: if the sparsest solution is sufficiently sparse, it can be found by linear programming. We explain this by the theory of convex polyt...

Numerical Solution of Fuzzy Linear Volterra Integral Equations of the Second Kind by Homotopy Analysis Method

Solving a System of Linear Equations by Homotopy Analysis Method

‎In this paper‎, ‎an efficient algorithm for solving a system of linear‎ ‎equations based on the homotopy analysis method is presented‎. ‎The‎ ‎proposed method is compared with the classical Jacobi iterative‎ ‎method‎, ‎and the convergence analysis is discussed‎. ‎Finally‎, ‎two‎ ‎numerical examples are presented to show the effectiveness of the‎ ‎proposed method.‎

A Method to Estimate the Solution of a Weakly Singular Non-linear Integro-differential Equations by Applying the Homotopy Methods

Numerical Solution of Interval Linear Programming

This paper presents an algorithm for solving interval linear programming(ILP) problems. Interval inequality constraints and equality constraints are discussed separately. The aim of the paper is to show that (ILP) problems can be decomposed into two general linear programming(LP) by the monotonicity of (LP) problems , and we can gain the interval objective values. Finally, the proposed method h...