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# root(method=’df-sane’)

`scipy.optimize.``root`(fun, x0, args=(), method='df-sane', tol=None, callback=None, options={'disp': False, 'fnorm': None, 'sigma_0': 1.0, 'eta_strategy': None, 'sigma_eps': 1e-10, 'M': 10, 'line_search': 'cruz', 'fatol': 1e-300, 'func': None, 'maxfev': 1000, 'ftol': 1e-08})

  Solve nonlinear equation with the DF-SANE method

  See also

  For documentation for the rest of the parameters, see `scipy.optimize.root`

  Options:

  ftol : float, optional

  > Relative norm tolerance.

  fatol : float, optional

  > Absolute norm tolerance. Algorithm terminates when `||func(x)|| < fatol + ftol ||func(x_0)||`.

  fnorm : callable, optional

  > Norm to use in the convergence check. If None, 2-norm is used.

  maxfev : int, optional

  > Maximum number of function evaluations.

  disp : bool, optional

  > Whether to print convergence process to stdout.

  eta_strategy : callable, optional

  > Choice of the `eta_k` parameter, which gives slack for growth of `||F||**2`. Called as `eta_k = eta_strategy(k, x, F)` with k the iteration number, x the current iterate and F the current residual. Should satisfy `eta_k > 0` and `sum(eta, k=0..inf) < inf`. Default: `||F||**2 / (1 + k)**2`.

  sigma_eps : float, optional

  > The spectral coefficient is constrained to `sigma_eps < sigma < 1/sigma_eps`. Default: 1e-10

  sigma_0 : float, optional

  > Initial spectral coefficient. Default: 1.0

  M : int, optional

  > Number of iterates to include in the nonmonotonic line search. Default: 10

  line_search : {‘cruz’, ‘cheng’}

  > Type of line search to employ. ‘cruz’ is the original one defined in [Martinez & Raydan. Math. Comp. 75, 1429 (2006)], ‘cheng’ is a modified search defined in [Cheng & Li. IMA J. Numer. Anal. 29, 814 (2009)]. Default: ‘cruz’

  References

  [R594] | “Spectral residual method without gradient information for solving large-scale nonlinear systems of equations.” W. La Cruz, J.M. Martinez, M. Raydan. Math. Comp. 75, 1429 (2006).

  [R595]

  23. La Cruz, Opt. Meth. Software, 29, 24 (2014).

  [R596]

  23. Cheng, D.-H. Li. IMA J. Numer. Anal. 29, 814 (2009).