Generalized Inverse Computation Based on an Orthogonal Decomposition Methodology
Patricia Gómez, Beatriz Lacruz, Rosa Eva Pruneda · Birkhäuser Boston eBooks · 2008
The need to compute the generalized inverse of a matrix appears in several statistical, mathematical and engineering problems, such as the estimation of linear classification and regression functions, electrical circuits estimation, calculus of structures, etc. In this paper, we propose to apply an orthogonal decomposition methodology to compute a weak generalized inverse, based on the calculus of a non-singular submatrix of the given matrix. Special attention will be focussed on the updating of the generalized inverse when some of the elements of the original matrix are modified. The proposed method allows us to perform this updating without starting the process from scratch. The proposed procedures will be illustrated with some examples and their application to the estimation of linear regression coefficients when a problem of multicollinearity is present.