Simoncini V., Elden L. Inexact Rayleigh quotient-type methods for subspace tracking. Technical report ercim.cnr.ian//1999-1172, 1999. |

Abstract (English) |
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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