Computable Accurate Upper and Lower Error Bounds for Approximate Solutions of Linear Algebraic Systems
Thomas J. Aird, Robert E. Lynch · ACM Transactions on Mathematical Software · 1975
Six bounds are considered on a norm of x -y, where x is the solution of a nonsingular linear system, A x ---b, and where y is an estimate of x.Methods are described for computing one of these.[[Crll/(1-k T) <[Ix-yll <--[[ Cr [[/(1-T) <(l+T)/(1--T)[Ix--yllifT = IICA -I[[ < 1, where C "~ A-1 and r = b -Ay.In addition to supplying upper and lower bounds, this gives very accurate error estimates which are orders of magnitude smaller than those obtained from other bounds.