Computation of multiple eigenvalues of infinite tridiagonal matrices

Computation of multiple eigenvalues of infinite tridiagonal matrices

In this paper, it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues. The computation of such double eigenvalues is enabled by the Newton method of two variables. The three-term recurrence relations obtained from its eigenvalue problem (EVP) subsume the well-known relations of (A) the zeros of Jν(z); (B) the zeros of zJ ′ ν(z)...

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.

Eigenvalues and eigenvectors of tridiagonal matrices

This paper is continuation of previous work by the present author, where explicit formulas for the eigenvalues associated with several tridiagonal matrices were given. In this paper the associated eigenvectors are calculated explicitly. As a consequence, a result obtained by WenChyuan Yueh and independently by S. Kouachi, concerning the eigenvalues and in particular the corresponding eigenvecto...

Ela Eigenvalues and Eigenvectors of Tridiagonal Matrices

This paper is continuation of previous work by the present author, where explicit formulas for the eigenvalues associated with several tridiagonal matrices were given. In this paper the associated eigenvectors are calculated explicitly. As a consequence, a result obtained by WenChyuan Yueh and independently by S. Kouachi, concerning the eigenvalues and in particular the corresponding eigenvecto...

Parallel Computation of Eigenvalues of Real Matrices