Local convergence analysis of tensor methods for nonlinear equations (Q1321657)

The authors analyze the local convergence of two versions of tensor methods, on problems where the Jacobian at the root has a null space of rank one. It is shown that under mild conditions the sequence of iterates converges locally and two or three-step \(Q\)-superlinearly to the solution with \(Q\)-order 3/2, while standard methods converge linearly with constant converging to 1/2. The paper also confirms that tensor methods converge at least quadratically on problems where the Jacobian at the root is nonsingular.