On the convergence of the quadratic method

Abstract

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