From: Allen Abrahamson Subject: Re: accuracy of computed matrix inverse Date: Sun, 05 Nov 2000 03:40:32 GMT Newsgroups: sci.math.num-analysis Summary: [missing] In article <8u2goa$ce1$1@nnrp1.deja.com>, mittelmann@asu.edu wrote: > You can get an exact inverse for nearly all matrices with iterative > refinement, but that does require partial double precision. Regarding the issue of iterative refinement, and its efficacy with respect to precision of the original inversion: Say that we use the iterative formulation (V_i are a series of numerical inverses, M is the exact original matrix): V_{i+1} = V_i + V_i (I - M V_i ). The case is not doing a refinement of a linear solution vector, but only of the inverse itself. Question: If this iteration is to be carried out in precision d (.ge. 0) digits better than that used to obtain V_0, then, in general, what may be said, a priori, about the ultimate "improvement", as measured by properties of (I - M V_{i+1})? Allen ------------------------------------------------------------------------ > In article , > prussing@aae.uiuc.edu (John Prussing) wrote: > > One way to test the accuracy of a computed matrix inverse is obviously > > to multiply the computed inverse by the original matrix and see how > > close the product is to the identity matrix. > > > > 1) Is this the best way? > > > > 2) If some additional property exists, say the determinant is equal to > > 1, can this be used to enhance the accuracy of the computed inverse? > > -- > > =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= > > John E. Prussing > > Dept. of Aeronautical & Astronautical Engineering > > University of Illinois at Urbana-Champaign > > http://www.uiuc.edu/~prussing > > =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= > > > > Sent via Deja.com http://www.deja.com/ > Before you buy. > Sent via Deja.com http://www.deja.com/ Before you buy.