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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) < [ I x yll <-[[ Cr [ [ / ( 1 T) < ( l + T ) / ( 1 T ) [ I x y l l i f T = I I C A 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.

Computable Accurate Upper and Lower Error Bounds for Approximate Solutions of Linear Algebraic Systems