We present one more algorithm to compute the condition number (for inversion) of a nn tridiagonal matrix J in O(n) time. Previous O(n) algorithms for this task given by Higham in 17] are based on the tempting compact representation of the upper (lower) triangle of J ?1 as the upper (lower) triangle of a rank-one matrix. However, they suuer from severe overrow and underrow problems, especially o...

Some new upper and lower bounds on determinants are presented for diagonally dominant matrices and general H-matrices by using different methods. These bounds are some improvements of results given by Ostrowski 1952 and 1937 , Price 1951 , Wang and Zhang 2002 , Huang and Liu 2005 , and so forth. In addition, these bounds are also used to localize some numerical characters e.g., the minimum eige...

113–123] proved that the convergence rate of the preconditioned Gauss–Seidel method for irreducibly diagonally dominant Z-matrices with a preconditioner I + S α is superior to that of the basic iterative method. In this paper, we present a new preconditioner I + K β which is different from the preconditioner given by Kohno et al. and prove the convergence theory about two preconditioned iterati...

Our aim is to characterize those matrices that are the response matrix of a semi–positive definite Schrödinger operator on a circular planar network. Our findings generalize the known results and allow us to consider both nonsingular and non diagonally dominant matrices as response matrices. To this end, we define the Dirichlet–to–Robin map associated with a Schrödinger operator on general netw...

The notion of accretive operator (see [1], [2]) plays an important part in the study of nonlinearsemigroups. According to this notion, we set up in the present study, essential properties of accretivity which allow to connect the set of linear accretive operators defined in a finite dimensional space with the set of M-matrix (see [3]). Such results allow us on one hand to make a link between va...

In this paper, we consider the localization of generalized eigenvalues, and we discuss ways in which the Gersgorin set for generalized eigenvalues can be approximated. Earlier, Stewart proposed an approximation using a chordal metric. We will obtain here an improved approximation, and using the concept of generalized diagonal dominance, we prove that the new approximation has some of the basic ...

We show in this note how support preconditioners can be applied to a class of linear systems arising from use of the finite element method to solve linear elliptic problems. Our technique reduces the problem, which is symmetric and positive definite, to a symmetric positive definite diagonally dominant problem. Significant theory has already been developed for preconditioners in the diagonally ...

Abstract. In this paper, some new lower bounds for the smallest singular value of a square complex matrix A are derived. A key tool to obtain these bounds is using some Hermitian matrices which are, in the sense of Loewner matrix ordering, below the Hermitian part of A or, more generally, below the Hermitian part of the unitary equivalences of A. Two types of new bounds are proposed. The first ...

In this note we show how to improve some recent upper and lower bounds for the elements of the inverse of diagonally dominant tridiagonal matrices. In particular, a technique described by [R. Peluso, and T. Politi, Some improvements on two-sided bounds on the inverse of diagonally dominant tridiagonal matrices, Lin. Alg. Appl. Vol. 330 (2001) 1-14], is used to obtain better bounds for the diago...