Abstract – Analysis of time series data can involve the inversion of large covariance matrices. For the class of ARMA (p, q) processes there are no exact explicit expressions for these inverses, except for the MA (1) process. In practice, the sample covariance matrix can be very large and inversion can be computationally time consuming and so approximate explicit expressions for the inverse are...

This paper studies open-loop tracking and feedback stabilization for nonholonomic systems. Using the concept of approximate inversion, results for drift-free, left-invariant systems on speciic matrix Lie groups are presented .

This paper studies open-loop tracking and feedback stabilization for nonholonomic systems. Using the concept of approximate inversion, results for drift-free, left-invariant systems on speciic matrix Lie groups are presented .

Approximate projection methods are useful computational tools for solving the equations of timedependent incompressible flow. In this report we will present a new discretization of the approximate projection in an approximate projection method. The discretizations of divergence and gradient will be identical to those in existing approximate projection methodology using cell-centered values of p...

It will be shown that extended Krylov subspaces –under some assumptions– can be retrieved without any explicit inversion or system solves involved. Instead we do the necessary computations of A−1v in an implicit way using the information from an enlarged standard Krylov subspace. It is well-known that both for classical and extended Krylov spaces, direct unitary similarity transformations exist...

The classical condition number is a very rough measure of the effect of perturbations on the inverse of a square matrix. First, it assumes that the perturbation is infinitesimally small. Second, it does not take into account the perturbation structure (e.g., Vandermonde). Similarly, the classical notion of the inverse of a matrix neglects the possibility of large, structured perturbations. We d...