Core Problems in Linear Algebraic Systems

Algebraic Solving of Complex Interval Linear Systems by Limiting ‎Factors‎

In this work, we propose a simple method for obtaining the algebraic solution of a complex interval linear system where coefficient matrix is a complex matrix and the right-hand-side vector is a complex interval vector. We first use a complex interval version of the Doolittle decomposition method and then we restrict the Doolittle's solution, by complex limiting factors, to achieve a complex in...

Algebraic multigrid methods for constrained linear systems with applications to contact problems in solid mechanics

This article develops a general framework for applying algebraic multigrid techniques to constrained systems of linear algebraic equations that arise in applications with discretized PDEs. We discuss constraint coarsening strategies for constructing multigrid coarse grid spaces and several classes of multigrid smoothers for these systems. The potential of these techniques is investigated with t...

On Algebraic Simplifications of Linear Functional Systems

In this paper, we show how to conjointly use module theory and constructive homological algebra to obtain general conditions for a matrix R of functional operators (e.g., differential/shift/time-delay operators) to be equivalent to a block-triangular or block-diagonal matrix R (i.e., conditions for the existence of unimodular matrices V and W satisfying that R = V R W ). These results allow us ...

SENSITIVITY ANALYSIS IN LINEAR-PLUS-LINEAR FRACTIONAL PROGRAMMING PROBLEMS

In this paper, we study the classical sensitivity analysis when the right - hand – side vector, and the coefficients of the objective function are allowed to vary. 

Solution of Systems of Linear Algebraic Equations