Local convergence analysis of tensor methods for nonlinear equations
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.
scientific article; zbMATH DE number 558704
scientific article