The decompositional approach to matrix computation

11 1951, Paul S. Dwyer pnblishcd I,inenr Comptntions, perhaps the first hook dcvoted cntirely to numerical linear algebra.' Digital conipiiting was in its infancy, and Dwyer focused on computation with tncchanical calculators. Nonctheless, the hook was state of the art. Figurc 1 reproduces a pagc of thc book dealing with Gaussian elimination. In 1954, Alston S. Householder published Prim+ p b nf Nzc"cn1 Ann1ysi.r; one of the first modcrn treatments of high-spccd digital coinputation. Figure 2 rcproduccs a page from this hook, also dealing with Gaussian elimiiiation. The contrast between tlicse two pages is striking. l'he most obvious difference is that Ilwyer