We prove convergence for the basic LR algorithm on a real unreduced tridiagonal matrix with a one-point spectrum the Jordan form is one big Jordan block. First we develop properties of eigenvector matrices. We also show how to deal with the singular case.

1: We show that certain integral positive definite symmetric tridiagonal matrices of determinant n are in one to one correspondence with elements of (Z/nZ)∗. We study some properties of this correspondence. In a somewhat unrelated second part we discuss a construction which associates a sequence of integral polytopes to every integral symmetric matrix.

In this short note, we present a novel method for computing exact lower and upper bounds of a symmetric tridiagonal interval matrix. Compared to the known methods, our approach is fast, simple to present and to implement, and avoids any assumptions Our construction explicitly yields those matrices for which particular lower and upper bounds are attained.

In this paper, we consider an inverse problem with the k-tridiagonal Toeplitz matrices. A theoretical result is obtained that under certain assumptions the explicit inverse of a ktridiagonal Toeplitz matrix can be derived immediately. Two numerical examples are given to demonstrate the validity of our results. (c) ٢٠١٢ Elsevier Ltd. All rights reserved.

We introduce the notion of a mock tridiagonal system. This is a generalization of a tridiagonal system in which the irreducibility assumption is replaced by a certain nonvanishing condition. We show how mock tridiagonal systems can be used to construct tridiagonal systems that meet certain specifications. This paper is part of our ongoing project to classify the tridiagonal systems up to isomor...

In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODEIVPs or ODE-BVPs. The approach is based on the concept of parallel factorization of a (block) tridiagonal matrix. This allows to obtain efficient parallel extensions of many known matrix factorizations, and to derive, as a by-product, a unifying approach to the parallel solution ...

We establish upper and lower bounds for the entries of the inverses of diagonally dominant tridiagonal matrices. These bounds improve the bounds recently given by Shivakumar and Ji. Moreover, we show how to improve our bounds iteratively. For an n n M{matrix this iterative reenement yields the exact inverse after n ? 1 steps.

In this paper, we firstly present a general expression for the entries of the th r   N r power of certain -square n are complex tridiagonal matrix, in terms of the Chebyshev polynomials of the first kind. Secondly, we obtain two complex factorizations for Fibonacci and Pell numbers. We also give some Maple 13 procedures in order to verify our calculations.

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A∗ : V → V that satisfy (i), (ii) below: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A∗ is diagonal. (ii) There exists a basis for V with respect to which ...

We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to operators. In the class of discussed here transformation is given by a Hermitian, positive-definite, diagonal operator. there an important difference between open boundary conditions and periodic ones. illustrate theoretical results means two simple, widely used, mod...