The calculation of the latent roots and vectors of matrices on the pilot model of the A.C.E.

Abstract

ABSTRACTThe problem of finding the latent roots and vectors of matrices has been treated in a number of papers ((2)–(7)) mainly from the point of view of desk computers. In this paper the problem is treated from the standpoint of users of high-speed automatic computers. In the first section a number of iterative processes are described and, in the second, the techniques developed for using these processes on the Pilot Model of the Automatic Computing Engine. It is shown that the methods give very high accuracy and can be used to deal with matrices of high orders even on a machine of very limited storage capacity. They have been used on numerous matrices of orders up to 60 mainly on problems arising in the aircraft industry and on eigenvalue problems for systems of ordinary differential equations.