material balance by linear equations

Material Balance by Linear Equations

Material Balance around process has been conducted by using mixer output equations. A method based on Mason's theory has been proposed to develop mixer output equations.

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.‎

Supplementary Material : Model Selection by Linear Programming

Duality in linear interval equations

In this paper we nd solution of linear interval equation in dual form based on the generalizedprocedure of interval extension which is called interval extended zero method.Moreover, proposed method has signicant advantage, is that it substantially decreasesthe excess width eect.

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...

Solving Linear Matrix Equations by Matrix Decompositions

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided. Keywords—Matrix equation, Generalized inverse, Generalized singular-value decomposition.