The first annual large dense linear system survey

In the March 24, 1991 issue of NA Digest, I submitted a questionnaire asking who was solving large dense linear systems of equations. Based on the responses, nearly all large dense linear systems today arise from either the benchmarking of supercomputers or applications involving the influence of a two dimensional boundary on three dimensional space. Not surprisingly, the area of computational aerodynamics or aero-electromechanics represents an important commercial application requiring the solution of such systems. The largest unstructured matrix that has been factored using Gaussian Elimination was a complex matrix of size 55,296. The largest dense matrix solved on a Sun using an iterative method was a real matrix of size 20,000. It is unclear at this time whether dense methods are truly needed at all for huge matrices. It is intended to survey users every year with the hope of including more applications as I am made aware of them.