On the convergence of the quadratic method
Lyonell Boulton, Aatef D. Hobiny · IMA Journal of Numerical Analysis · 2015
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 Schrödinger operators.