On the convergence of a new Rayleigh quotient method with applications to large eigenproblems
A variant of the Rayleigh quotient method is proposed to compute an eigenvalue and corresponding eigenvectors of a matrix. This variant called singular vector Rayleigh quotient method uses the observation that eigenvectors of a matrix with eigenvalue zero are also singular vectors corresponding to zero singular values. If these singular vectors are computed exactly the method is quadratically convergent. But exact singular vectors are not required for convergence. The method may be useful for large eigenvalue problems. The decomposition associated with a simple eigenvalue, the generalized Rayleigh quotients, and the convergence of the algorithm are discussed. Implicitly in the analysis is a relation between the inferior singular vector of the matrix and an eigenvector corresponding to a small eigenvalue.
singular vector Rayleigh quotient method
scientific article; zbMATH DE number 1249444