Singular Perturbations of Linear Operators

• With my colleague K. Avrachenkov from INRIA (Sophia-Antipolis) we have developed a methodology to compute inverses of nearly singular linear operators, described in: K. Avrachenkov and J.B. Lasserre. Analytic perturbation of generalized inverses, Linear Algebra & Appl. 438 (2013), pp. 1793--1813 

This method has been implemented recently in : 

• Laurent expansion of the inverse of perturbed, singular matrices, P. Gonzalez-Rodriguez, M. Moscoso, M. Kindelan. J. Computational Physics 299 (2015), pp. 307--319. 

and also in : 

• Laurent series based RBF-FD method to avoid ill-conditioning, P. Gonzalez-Rodriguez, V. Bayona, M. Moscoso, M. Kindelan. Engineering Analysis with Boundary Elements 52 (2015), pp. 24--31.  for computing accurately the inverse of the RBF (radial basis function) interpolation matrix.