LQ-Schur projection on large sparse matrix equations

LQ-Schur projection on large sparse matrix equations

Periodic Schur Form and Some Matrix Equations

We propose an elegant and conceptually simple method for computing the periodic solution of three classes of periodic matrix equations | Ric-cati, Lyapunov and Sylvester. Such equations arise naturally in several problems of linear system theory. Our approach is very attractive from a numerical point of view, since it is based on the periodic Schur form of techniques involving unitary (orthogon...

Applying Schur Complements for Handling General Updates of a Large, Sparse, Unsymmetric Matrix

We describe a set of procedures for computing and updating an inverse representation of a large and sparse unsymmetric matrix A. The representation is built of two matrices: an easily invertible, large and sparse matrix A0 and a dense Schur complement matrix S. An e cient heuristic is given that nds this representation for any matrix A and keeps the size of S as small as possible. Equations wit...

On lq estimation of sparse inverse covariance

Recently, major attention has been given to penalized log-likelihood estimators for sparse precision (inverse covariance) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex l1 norm. However, it is not always the case that the best estimator is achieved with this penalty. So, to improve sparsity and reduce biases associated with the l1 norm, one mu...

On Solving Large Algebraic Riccati Matrix Equations

In this paper, we present a numerical method for solving large continuous-time algebraic Riccati equations. This method is based on the global FOM algorithm and we call it by global FOM-Riccati-Like (GFRL) algorithm .