On the solution of ill-conditioned systems of linear equations

Zahra Vahedipour, Behrouz Daneshian

Abstract


In this paper we propose novel technique to solve the ill-conditioned system of linear equations Ax = b. For given a matrix, we find two invertible diagonal matrices  and  by Simulated Annealing method, such that

                                                                                       

 ( denoting the set of all diagonal matrices) relative to a given matrix norm. With this step carried out, the solution of the system  is effected by solving the system  and then calculating  .


Keywords


Simulated Annealing; Ill-conditioned matrix;Stochastic optimization.

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