On updating formulas for least squares solutions and pseudo-inverses

AbstractFor A : Vn → Vm with arbitrary inner products in Vn and Vm, updating formulas are given for the least squares solution of Ax = b and for the pseudo-inverse AI; an iterative scheme is given to calculate AI starting from an arbitrary initial guess B.When applied to matrices and ordinary inner products are assumed formulas of Greville and Fletcher are obtained. It is shown how Fletcher's formulas may be constructed from Greville's