solving ill-conditioned linear equations using simulated annealing method

The purpose of this paper is to using the simulated annealing method to solving a linear equations system which have an ill-conditioned coefficients matrix. a linear equation system is called ill-conditioned if its condition number be large. by using a matrix scaling, the linear equation system transforms into a linear equation system with less condition number. matrix balancing is performed by simulated annealing algorithm. the efficiency of this method is investigated by numerical examples. numerical results show that simulated annealing can reduce the condition number of equations.