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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 Schru007fodinger operators.
Regula Falsi, or the method of false position, is a numerical method for finding an approximate solution to f(x) = 0 on a finite interval [a, b], where f is a real-valued continuous function on [a, b] and satisfies f(a)f(b) < 0. Previous studies prov
We show that solutions of the chemical reaction-diffusion system associated to $A+Brightleftharpoons C$ in one spatial dimension can be approximated in $L^2$ on any finite time interval by solutions of a space discretized ODE system which models the
Boundary integral numerical methods are among the most accurate methods for interfacial Stokes flow, and are widely applied. They have the advantage that only the boundary of the domain must be discretized, which reduces the number of discretization
The randomized Gauss--Seidel method and its extension have attracted much attention recently and their convergence rates have been considered extensively. However, the convergence rates are usually determined by upper bounds, which cannot fully refle
We present a convergence proof for higher order implementations of the projective integration method (PI) for a class of deterministic multi-scale systems in which fast variables quickly settle on a slow manifold. The error is shown to contain contri