Acceleration of inexact inverse iteration for eigenvalue problems

Many methods have been used to improve the efficiency of iterative numerical algorithms. Combining different methods is not always possible because the performance of acceleration methods usually depends critically on the precise form of the error in successive iterates, and this form often changes when other acceleration methods are used. Inexact implementation methods have proved particularly effective in increasing the efficiency of iterations involving sparse matrices. This article investigates the extent to which the efficiency of inexact inverse iteration and the inexact Rayleigh quotient algorithm, for the numerical computation of eigenvalues and eigenvectors of sparse matrices, may be further increased by the use of the scalar epsilon algorithm, a classical extrapolation technique. Some encouraging numerical results are presented and some pointers are given for future research. References A. L. Andrew. The accuracy of Numerov's method for eigenvalues. 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