The convergence rates for the method of Weinstein and a variant method of
Aronszajn known as "truncation including the remainder" are derived in terms of
the containment gaps between exact and approximating subspaces, using analytical
techniques that arise in part in the convergence analysis of finite element methods
for differential eigenvalue problems. An example of a one dimensional Schrodinger
operator with a potential is presented which arises in quantum mechanics.
Examples using the recent eigenvector-free (EVF) method of Beattie and Goerisch
are considered. Since the EVF method uses finite element trial functions as approximating
vectors, it produces sparse and well-structured coefficient matrices. For these
large-order sparse matrix eigenvalue problems, we adapt a spectral transformation
Lanczos algorithm for finding a few wanted eigenvalues. For a few particular examples
of vibration in beams and plates, convergence behavior is experimentally evaluated.
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