On Regularization of I11-Conditioned Linear Systems

I11-conditioned linear systems may frequently arise in discretization of integral equationsand many other real world applications. Solving such systems by classical methods might tailor result to solutions that are meaningless from practical point view. Moreover a slightperturbation in the right hand side vector might also lead to an enormous change of the solutionvector due to ill-conditioned ness. To find meaningful solution of such systems. the Tikhonovregularization is an effective technique that has been widely used. In this paper we use it tosolve ill-conditioned linear system and also to find closest feasible linear systems to nearlyfeasible linear systems by smallest changes in problem data. Throughout the paper numericalresults are reported to demonstrate the practical efficiency of the presented algorithms.