A Stopping Criterion for the Iterative Solution of an Overdetermined System of Linear Algebraic Equations

摘要

For an overdetermined system of linear algebraic equations, systems obtained by introduc-ing independent random errors into the original right-hand side are examined. Under certain assump-tions on how these random variables are distributed, a practical stopping criterion is proposed for an iter-ative process that minimizes the sum of the squares of the residuals for the above systems. Numericalresults demonstrating the efficiency of this criterion for some ill-conditioned problems are presented.