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fsolve or nSolve with the option steffenson_solver

The Steffenson method is generically the fastest method.
It combines the Newton method with a "delta-two" Aitken acceleration : with the Newton method, we obtain the sequence xi and the convergence acceleration gives the Steffenson sequence

Ri = xi - $\displaystyle {\frac{{(x_{i+1} - x_i)^2}}{{ (x_{i+2} - 2 x_{i+1} + x_{i})}}}$

Input :
Output :

giac documentation written by Renée De Graeve and Bernard Parisse