OT05 research project
OT-05-40 RASTACO: Large RAnk STructured mAtrix COmputations (1-10-2005 to 30-09-2009)
Short description
Large matrix computations can be performed efficiently if one takes into consideration the underlying structure of the matrix. One of these structures is the rank structure. Here, the matrix has one or more submatrices having a rank lower than the expected generic rank of each of these submatrices. In this project, we will use this rank structure to develop efficient algorithms for computing the QR-decomposition and the LU-decomposition. These results will be developed using a general framework that we will construct for very general rank structured matrices. Once we can compute the QR-decomposition in a fast and accurate way, we can design (implicit as well as explicit) QR-algorithms to compute the eigenvalues and eigenvectors of a rank structured matrix. We will also extend our results to the generalized eigenproblem.
