Linear systems in matlab with zero residual
Several examples of linear systems are given for which the residual of the computed approximation (computed in working precision) is entirely zero. Nevertheless, the computed approximation by Matlab’s backslash operator is highly inaccurate, and often no warning is issued. Examples for matrix inversion in that spirit are given as well. Moreover, it is demonstrated that rounding the exact real result to the nearest floating-point numbers may be worse than using an approximation computed by some floating-point algorithm. Concluding, some advice is given to users and developers.