Mathematica: a system for doing mathematics by computer (2nd ed.)
Mathematica: a system for doing mathematics by computer (2nd ed.)
Accelerated convergence in Newton's method
SIAM Review
Accelerated Convergence in Newton's Method
SIAM Review
Numerical Methods Using MATLAB
Numerical Methods Using MATLAB
An efficient fifth order method for solving systems of nonlinear equations
Computers & Mathematics with Applications
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We study the efficiency of the accelerated Newton method (Garlach, SIAM Rev. 36 (1994) 272-276) for several orders of convergence versus Danby's method for the resolution of Kepler's equation; we find that the cited method of order three is competitive with Danby's method and the classical Newton's method. We also generalize the accelerated Newton method for the resolution of system of algebraic equations, obtaining a formula of order three and a proof of its convergence; its application to several examples shows that its efficiency is greater than Newton's method.