lanczos-type algorithms are well known for their inherent instability. they typically breakdown occurs when relevant orthogonal polynomials do not exist. current approaches to curing breakdown rely on jumping over the non-existent polynomials to resume computation. this may have to be used many times during the solution process. we suggest an alternative to jumping, which consists of restarting...

A method for calculating the strict Chebyshev solution of overdetermined systems of linear equations using linear programming techniques is described. This method provides: (1) a way to determine, for the majority of cases, all the equations belonging to the characteristic set, (2) an efficient method to obtain the inverse of the matrix needed to calculate the strict Chebyshev solution, and (3)...

Linear dynamic systems with output, evolving on the space R∞ of infinite sequences, are studied. They are described by infinite systems of ∆-differential linear equations with row-finite matrices, for which time belongs to an arbitrary time scale. Such systems generalize discrete-time and continuous-time row-finite systems on R∞, studied earlier. Necessary and sufficient condition on observabil...

This paper presents en algorithm for solving interval linear programming problems. The algorithm is a finite iterative method, which in each iteration solves a full row rank interval linear progranming problem, with only one additional constraint. The solution and/or problem chosen appears to be conputationally more efficient than that in the Ben-Israel and Robers algorithm.

Infinite–dimensional linear dynamic systems, with output, are studied. They are described by row-finite infinite matrices. Observability of such systems is investigated. It is shown that observability is equivalent to the property that one can calculate the value of each state variable using only finitely many rows of Kalman observability matrix. Different necessary or sufficient conditions of ...

We present an algorithm for computing a d-dimensional subspace of the row space of a matrix. For an n×n matrix A with m nonzero entries and with rank(A) ≥ d the algorithm generates a d × n matrix with full row rank and which is a subspace of Rows(A). If rank(A) < d the algorithm generates a rank(A)×n row-equivalent matrix. The running time of the algorithm is

In this paper we present an efficient algorithm for computing a sparse null space basis for a full row rank matrix. We first apply the ideas of the Markowitz’s pivot selection criterion to a rank reducing algorithm to propose an efficient algorithm for computing sparse null space bases of full row rank matrices. We then describe how we can use the Dulmage-Mendelsohn decomposition to make the re...