A semilocal convergence analysis for the method of tangent parabolas - Ioannis K. Argyros (Journal of Numerical Analysis and Approximation Theory, 2005)
We present a semilocal convergence analysis for the method of tangent parabolas (Euler-Chebyshev) using a combination of Lipschitz and center Lipschitz conditions on the Fréchet derivatives involved. This way we produce a majorizing sequence which converges under weaker conditions than before. The error bounds obtained are more precise and the information of the location of the solution better than in earlier results.