ABSTRACT
Cornelius Lanczos, a physicist and applied mathematician, had already been very successful at devising algorithms for analyzing a variety of mathematical models, and he was well acquainted with the challenges of computation on desk calculators. Lanczos turned his attention to the solution of linear systems of equations and matrix eigenvalue problems. He begins by noting that linear differential and integral operator equations can be solved by considering either of two series: the "Liouville-Neumann expansion," which only requires application of the operator but can suffer convergence difficulties; or the "Schmidt series," which is unconditionally convergent but requires knowledge of the eigensystem. Researchers such as George Forsythe, J. Barkley Rosser, and Magnus Hestenes were also thinking about eigenvalue problems and the solution of linear systems, and they proposed and tested a variety of approaches for "large" problems.
