The complete positivity of symmetric tridiagonal and pentadiagonal matrices

Fine Spectra of Tridiagonal Symmetric Matrices

Eigenvalues of symmetric tridiagonal interval matrices revisited

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.

Exponentials of Symmetric Matrices through Tridiagonal Reductions

A simple and efficient numerical algorithm for computing the exponential of a symmetric matrix is developed in this paper. For an n× n matrix, the required number of operations is around 10/3 n. It is based on the orthogonal reduction to a tridiagonal form and the Chebyshev uniform approximation of e−x on [0,∞).

Inner deflation for symmetric tridiagonal matrices

Suppose that one knows an accurate approximation to an eigenvalue of a real symmetric tridiagonal matrix. A variant of deflation by the Givens rotations is proposed in order to split off the approximated eigenvalue. Such a deflation can be used instead of inverse iteration to compute the corresponding eigenvector. © 2002 Elsevier Science Inc. All rights reserved.

On deflation for symmetric tridiagonal matrices

K.V. Fernando developed an efficient approach for computation of an eigenvector of a tridiagonal matrix corresponding to an approximate eigenvalue. We supplement Fernando’s method with deflation procedures by Givens rotations. These deflations can be used in the Lanczos process and instead of the inverse iteration.