International Conference on Mathematical and Statistical Modeling in Honor of Enrique Castillo. June 28-30, 2006 Generalized Inverse Computation Based on an Orthogonal Decomposition Methodology. PatriciaG´omez * Department of Applied Mathematics, University of Cantabria (Spain). Rosa E. Pruneda Department of Mathematics Castilla-La Mancha University (Spain). Beatriz Lacruz Department of Statistical Methods Zaragoza University (Spain). Abstract The need of computing the generalized inverse of a matrix appears in several statistical, mathematical and engineering problems, such as the estimation of lin- ear 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. This weak form will be used to com- pose other generalized inverses based on it. Special attention will be focussed on the generalized inverse updating when some of the elements of the original matrix are modified. The proposed method allows to perform this update without start the process from scratch. This ability will be relevant on the application of the generalized inverse to solve problems involving linear system of equations where the system has to be iteratively modified in some of its elements. Finally, the pro- posed procedure will be illustrated with some examples and its application to the estimation of regression functions. Key Words: Linear systems, Regression Functions, Updated Solutions 1 Introduction Castillo et al. (1999) have introduced a pivoting transformation for obtain- ing the orthogonal of a given linear subspace. This process decomposes the Euclidean Space in a direct sum of the orthogonal linear subspace and its complement. This method is applied to solve a long list of problems in linear algebra including the resolution of systems of linear equations. Some * Correspondence to: gomezp@unican.es