Istituto di Matematica Applicata e Tecnologie Informatiche     
Simoncini V., Elden L. Inexact Rayleigh quotient-type methods for subspace tracking. Technical report ercim.cnr.ian//1999-1172, 1999.
We are interested in the computation of the $s$ largest or smallest eigenvalues and corresponding eigenvectors of a Hermitian positive definite matrix $A in CC^{n times n}$, assuming that good approximations of the wanted eigenpairs are already available and that $sll n$, as is the case in applications such as signal processing and structural mechanics. We analyze efficient implementations of inexact Rayleigh quotient--type methods, which involve the approximate solution of a linear system at each iteration. We show that for $s=1$ the inexact version of the classical Rayleigh quotient iteration is mathematically equivalent to more recent approaches which employ projected equations. Generalizations to the case $s>1$ are also discussed. Ad--hoc preconditioning strategies are proposed to make the computation efficient for unfavorable spectral distributions. Results of numerical experiments on two significant examples are reported.
Subject Invariant subspace approximation, iterative methods, Newton method,Rayleigh Quotient iteration

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