anned by the gradient and the approximate Gauss-Newton step
found by ``scipy.sparse.linalg.lsmr``. A 2-D trust-region problem is
reformulated as a 4th order algebraic equation and solved very accurately by
``numpy.roots``. The subspace approach allows to solve very large problems
(up to couple of millions of residuals on a regular PC), provided the Jacobian
matrix is sufficiently sparse.

References
----------
.. [STIR] Branch, M.A., T.F. Coleman, and Y. Li, "A Subspace, Interior,
      and Conjugate Gradient Method for Large-Scale Bound-Constrained
      Minimization Problems," SIAM Journal on Scientific Computing,
      Vol. 21, Number 1, pp 1-23, 1999.
.. [JJMore] More, J. J., "The Levenberg-Marquardt Algorithm: Implementation
    and Theory," Numerical Analysis, ed. G. A. Watson, Lecture
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