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The Inexact Rayleigh Quotient Iteration for the Large Hermitian Matrix Eigenproblem

The inexact Rayleigh quotient iteration (RQI) is used for computing the smallest eigenpair of a large Hermitian matrix. It’s shown in this paper that under the uniform positiveness condition a new convergence theorem of the inexact RQI is presented and proved by the nature of eigenvalues. All the results are verified and analyzed by numerical experiments.