Estimates for Interior Eigenvalues of Large Nonsymmetric Matrices

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A new procedure will be investigated for extracting approximate eigenvalues and eigenvectors of a nonsymmetric matrix from a given subspace. It is assumed that it is impractical to factor the matrix. The procedure is related to the Rayleigh-Ritz procedure, but it gives better estimates for interior eigenvalues. It can improve convergence rates for the Arnoldi method, for preconditioning methods such as Davidson's method, and for other methods. These methods will be tested and compared.