The evaluation of eigenvalues and eigenvectors of real symmetric matrices by simultaneous iteration

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Abstract
A method is described of obtaining all or a subset of the eigenvalues and corresponding eigenvectors of real symmetric matrices by iterating simultaneously with a number of trial vectors. Its relationship with a previous simultaneous iteration method is discussed and the results of some numerical tests are given. These methods are useful in cases where a few of the dominant eigenvalues and eigenvectors of large matrices are required.