The minimal 2-norm solution to an underdetermined system Ax b of full rank can be computed using a QR factorization of AT in two different ways. One method requires storage and reuse of the orthogonal matrix Q, while the method of seminormal equations does not. Existing error analyses show that both methods produce computed solutions whose normwise relative error is bounded to first order by ca...

This communication deals with the problem of state estimation for a class of non linear singular systems. Sufficient conditions for the existence of such observers are provided and the design of an observer is examined. Assuming that the measurement matrix is full row rank involves many calculation simplifications ; therefore special emphasis in the computational aspect of the observer matrices...

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 A 0 and a dense Schur complement matrix S. An eecient heuristic is given that nds this representation for any matrix A and keeps the size of S as small as possible. Equations wi...

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...

The complexity of performing matrix computations, such as solving a linear system, inverting a nonsingular matrix or computing its rank, has received a lot of attention by both the theory and the scientiic computing communities. In this paper we address some \nonclassical" matrix problems that nd extensive applications, notably in control theory. More precisely, we study the matrix equations AX...

In this paper we propose a new numerically reliable computational approach to determine the inner-outer factorization of a rational transfer matrix G of a linear descriptor system. In contrast to existing computationally involved “one-shot” methods which require the solution of Riccati or generalized Riccati equations, the new approach relies on an efficient recursive zeros dislocation techniqu...

Several problems in compressed sensing and randomized tensor decomposition can be formulated as a structured linear system with constrained the solution. In particular, we consider block row Kronecker-structured systems low multilinear rank singular value decomposition, low-rank canonical polyadic or train this paper, provide algorithms that serve tools for finding such solutions large, higher-...