Dedicated to our friends Beresford and Velvel on the occasion of their sixtieth birthdays. ABSTRACT We show that a certain matrix norm ratio studied by Parlett has a supremum that is O(p n) when the chosen norm is the Frobenius norm, while it is O(log n) for the 2-norm. This ratio arises in Parlett's analysis of the Cholesky decomposition of an n by n matrix.

Under one-sided conditions, we establish explicit expressions for the condition numbers of core inverse and solution a linear system, using Hartwig Spindelb?ck?s decomposition, spectral norm Frobenius norm. We also present structured perturbation inverse.

An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations AXB − CYD,EXF − GYH M,N , which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices X and Y . When the matrix equations are consistent, for any initial generalized reflexive matrix pair X1, Y1 , the generalized reflexive solutions can be obtained b...

The general coupled matrix equations (including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory. In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations over reflexive matrix solution. When the general coupled matrix equations are consistent over reflexive matrices, the reflex...

this article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. we present a concrete formulation for the frobenius norm of the classical wavelet transforms over finite fields. it is shown that each vector defined over a finite field can be represented as...

In this paper we introduce a new method for defining preconditioners for the iterative solution of a system of linear equations. By generalizing the class of modified preconditioners (e.g. MILU), the interface probing, and the class of preconditioners related to the Frobenius norm minimization (e.g. FSAI, SPAI) we develop a toolbox for computing preconditioners that are improved relative to a g...