BroydenFirst#
- class scipy.optimize.BroydenFirst(alpha=None, reduction_method='restart', max_rank=None)[source]#
- Find a root of a function, using Broyden’s first Jacobian approximation. - This method is also known as “Broyden’s good method”. - Parameters:
- %(params_basic)s
- %(broyden_params)s
- %(params_extra)s
 
 - Methods - aspreconditioner - matvec - rmatvec - rsolve - setup - solve - todense - update - See also - root
- Interface to root finding algorithms for multivariate functions. See - method='broyden1'in particular.
 - Notes - This algorithm implements the inverse Jacobian Quasi-Newton update \[H_+ = H + (dx - H df) dx^\dagger H / ( dx^\dagger H df)\]- which corresponds to Broyden’s first Jacobian update \[J_+ = J + (df - J dx) dx^\dagger / dx^\dagger dx\]- References [1]- B.A. van der Rotten, PhD thesis, “A limited memory Broyden method to solve high-dimensional systems of nonlinear equations”. Mathematisch Instituut, Universiteit Leiden, The Netherlands (2003). https://math.leidenuniv.nl/scripties/Rotten.pdf - Examples - The following functions define a system of nonlinear equations - >>> def fun(x): ... return [x[0] + 0.5 * (x[0] - x[1])**3 - 1.0, ... 0.5 * (x[1] - x[0])**3 + x[1]] - A solution can be obtained as follows. - >>> from scipy import optimize >>> sol = optimize.broyden1(fun, [0, 0]) >>> sol array([0.84116396, 0.15883641])