On Quotient-Convergence Factors

On Quotient-convergence Factors

Convergence Analysis of Inexact Rayleigh Quotient Iteration

We consider the computation of the smallest eigenvalue and associated eigenvector of a Hermitian positive definite pencil. Rayleigh quotient iteration (RQI) is known to converge cubically, and we first analyze how this convergence is affected when the arising linear systems are solved only approximately. We introduce a special measure of the relative error made in the solution of these systems ...

Effect of environmental factors on intelligence quotient of children

INTRODUCTION A child's intelligence quotient (IQ) is determined by both genetic and environmental factors that start from the prenatal period itself. There is a lack of data on the factors which influence IQ in Indian children; therefore, we conducted a multicenter questionnaire-based study to determine the environmental factors which influence IQ in Indian children. PARTICIPANTS AND METHODS ...

Convergence of Inexact Rayleigh Quotient Iterations and Jacobi-davidson

We consider the computation of the smallest eigenvalue and associated eigenvector of a an Hermitian positive definite pencil. Rayleigh quotient iterations (RQI) are known to converge cubically and we first analyze how this convergence is affected when the arising linear systems are solved only approximately. We obtain an upper bound on the convergence factor which we show to be sharp for a wide...

A Block Rayleigh Quotient Iteration with Local Quadratic Convergence

We present an iterative method, based on a block generalization of the Rayleigh Quotient Iteration method, to search for the p lowest eigenpairs of the generalized matrix eigenvalue problem Au = Bu. We prove its local quadratic convergence when B A is symmetric. The benefits of this method are the well-conditioned linear systems produced and the ability to treat multiple or nearly degenerate ei...