In this paper we construct a few iterative processes for computing -inverses of a linear bounded operator. These algorithms are extensions of the corresponding algorithms introduced in [11] and a method from [8]. A few error estimates are derived.
The question of generalizing results involving chordal graphs to similar concepts for chordal bipartite graphs is addressed. First, it is found that the removal of a bisimplicial edge from a chordal bipartite graph produces a chordal bipartite graph. As consequence, occurance of arithmetic zeros will not terminate perfect Gaussian elimination on sparse matrices having associated a chordal bipartite graph. Next, a property concerning minimal edge separators is presented. Finally, it is shown that,...
We present an extension of the QR method to simultaneously compute the joint eigenvalues of a finite family of commuting matrices. The problem is motivated by the task of finding solutions of a polynomial system. Several examples are included.
It is proved that generalized polynomials with rational exponents over a commutative field form an elementary divisor ring; an algorithm for computing the Smith normal form is derived and implemented.
In the paper, a method is given for finding all solutions of a system of linear equations with interval coefficients and with additional supposition that these coefficients fulfil a given system of homogeneous linear equations.
Linear matrix approximation problems are often solved by the total least squares minimization (TLS). Unfortunately, the TLS solution may not exist in general. The so-called core problem theory brought an insight into this effect. Moreover, it simplified the solvability analysis if is of column rank one by extracting a core problem having always a unique TLS solution. However, if the rank of is larger, the core problem may stay unsolvable in the TLS sense, as shown for the first time by Hnětynková,...
A finite iteration method for solving systems of (max, min)-linear equations is presented. The systems have variables on both sides of the equations. The algorithm has polynomial complexity and may be extended to wider classes of equations with a similar structure.