Effect of Propagated Error on Inverse of Hilbert Matrix

where E are the initial errors of the elements of the matrix A. These errors may be due to the finite representation of numbers in some base, such as ] represented in the base two; or the data may contain errors of measurement. I t is essential to know what effect these errors have on the values of a resultant solution. This is particularly valuable in the case of "il l-conditioned" matrices where a serious loss of significant figures may occur during the computational procedure.