As computers grow in power and speed, matrices grow in size. In 1968,
practical production calculations with linear algebraic systems of order 5000
were commonplace, while a "large" system was one of order 10000 or more. 1
In 1978, an overdetermined problem with 2.5 million equations in 400000
unknowns was reported/ in 1981, the magnitude of the same problem had
grown: it had 6000000 equations, still in 400000 unknowns. 3 The matrix of
coefficients had 2.4 x 1012 entries, most of which were zero: it was a sparse
matrix. A similar trend toward increasing size is observed in eigenvalue
calculations, where a "large" matrix is one of order 4900 or 12000. 4 Will
matrix problems continue to grow even further? Will our ability to solve
them increase at a sufficiently high rate?