On the convergence of the quadratic method
Provides improved convergence guarantees for eigenvalue computation in quantum mechanics and spectral theory, but is incremental as it refines existing bounds.
The paper derives explicit asymptotic bounds for the convergence of the quadratic method for eigenvalue enclosures of self-adjoint operators, showing significant improvement over previous bounds. Numerical experiments on 1D Schrödinger operators confirm the theory.
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.