A variant of the fixed tangent method for spectral computations on integral operators

We propose a variant of the standard fixed tangent iteration to compute eigenvalues and corresponding invariant subspaces of a linear integral compact operator T defined on the space of complex valued continuous functions defined in [0, 1]. Convergence holds under very weak hypotheses on some discretization T n of T which is used for computing both the starting point of iterations and an approximation to the derivative. Numerical experiments are performed with integral operators defined either by a continuous kernel or by a weakly singular kernel.