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Bounded-Norm Matrix-Inverse Mappings

This paper introduces the concept of bounded-norm matrix-inverse mappings, i.e. mappings μ: R m×n →R nxm such that, for all nonzero m×n matrices A, the matrix μ(A) is a generalized inverse of A and ||μ(A)|| 0 is a constant and s(A) in the nonzero singular value of A having smallest absolute value. It is shown how the definition of such mappings is motivated by the need to ensure finite termination of the inner-iterations of generalized elimination methods for the solution of nonlinearly constrained optimization problems. The main result of the paper is that the mapping defined by μ(A)=A b is a bounded-norm matrix-inverse mapping, provided that the basic inverse A b is calculated using Gaussian elimination with complete pivoting