arXiv:1307.0313 Abstract | arXiv Analytics

arXiv:1307.0313 [math.NA]Abstract References Reviews Resources

On the convergence of the quadratic method

Published 2013-07-01, updated 2014-08-05Version 2

The convergence of the so-called quadratic method for computing eigenvalue enclosures of general self-adjoint operators is examined. Explicit asymptotic bounds for convergence to isolated eigenvalues are found. These bounds turn out to improve signi?cantly upon those determined in previous investigations. The theory is illustrated by means of several numerical experiments performed on particularly simple benchmark models of one-dimensional Schrodinger operators.

Comments: Main result extended to isolated eigenvalues of general self-adjoint operators. Two gaps in proofs and many typos corrected

Categories: math.NA

Subjects: 34L15, 35P15

Keywords: quadratic method, convergence, one-dimensional schrodinger operators, general self-adjoint operators, explicit asymptotic bounds

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