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Generalizationsīroyden’s method is a generalization of the secant method to more than one dimension. If, however, we consider parallel processing for the evaluation of the derivative, Newton’s method proves its worth, being faster in time, though still spending more steps. ![]() This result only holds under some technical conditions, namely that takes as much time as evaluating its derivative and we neglect all other costs, we can do two steps of the secant method (decreasing the logarithm of the error by a factor φ 2 ≈ 2.6) for the same cost as one step of Newton’s method (decreasing the logarithm of the error by a factor 2), so the secant method is faster. ![]() ![]() In particular, the convergence is superlinear, but not quite quadratic.
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