A bandstructure-invariant deflation for real symmetric matrices

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.

Spectral Functions for Real Symmetric Toeplitz Matrices

We derive separate spectral functions for the even and odd spectra of a real symmetric Toeplitz matrix, which are given by the roots of those functions. These are rational functions, also commonly referred to as secular functions. Two applications are considered: spectral evolution as a function of one parameter and the computation of eigenvalues.

Invariant Symmetric Block Matrices for the Design of Mixture Experiments

Real Invariant Matrices and Flavour-Symmetric Mixing Variables with Emphasis on Neutrino Oscillations

In fermion mixing phenomenology, the matrix of moduli squared, P = (|U |2), is well-known to carry essentially the same information as the complex mixing matrix U itself, but with the advantage of being phase-convention independent. The matrix K (analogous to the Jarlskog CP -invariant J) formed from the real parts of the mixing matrix “plaquette” products is similarly invariant. In this paper,...