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Convergence of the Ulm-like method under the Hölder condition. (English) Zbl 1339.65070

Summary: We study the convergence problem of an Ulm-like method for solving nonlinear operator equations without computing (approximate) Jacobian matrices and solving (approximate) Jacobian equations. Under the assumption that the first Fréchet derivative satisfies the Hölder condition, the Ulm-like method yields superlinear convergence. A numerical example is provided to demonstrate the efficacy of our convergence analysis.

MSC:

65H10 Numerical computation of solutions to systems of equations
65J15 Numerical solutions to equations with nonlinear operators
47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
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