Computational aspects of matrix generalized inversion for the computer with applications

AbstractNumerous theoretical problems have been simplified and, in many cases, unified via the theory of matrix generalized inversion, but not withstanding storage difficulties, occasionally, at the time of computer utilization. The sizes of matrices encountered may, in some cases, be too large for standard manipulations using existing routines. The purpose of this paper is to present some computational aspects of matrix generalized inversion for computer manipulations which provide partial relief to such problems, along with a discussion of some applications, particularly in the area of statistical analyses. Partial relief may be had, for example, through the utilization of the matrix kronecker product and its associated properties, special storage processes such as those available in manipulations with sparse matrices, and schemes for computing the matrix generalized inverse of partitioned matrices. In particular, a procedure for recursive partitioning is developed which permits the Moore Penrose inversion of matrices of any (finite) order