Restricted rank modification of the symmetric eigenvalue problem: Theoretical considerations

Abstract

The problem is considered how to obtain the eigenvalues and vectors of a matrix A+VVT where A is a symmetric matrix with known spectral decomposition and VVT is a positive semidefinite matrix of low rank. It is shown that the eigenvalues of A+VVT can easily be located to any desired accuracy by means of the inertia of the matrix I - VT(λ - A)-1V. The problem of determining the eigenvalues of A restricted to R(V)⊥ can be treated likewise. © 1988.