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44 [NocedalWright]_. At each iteration, the approximation is solved to
46 non-linear least squares, an approximation can be constructed by using
232 approximation if we restrict ourselves to moving along the direction
253 Levenberg-Marquardt solves the linear approximation from scratch with
378 Here :math:`H(x)` is some approximation to the Hessian of the
406 dimensions in which a full, dense approximation to the inverse
411 4. ``LBFGS`` A limited memory approximation to the full ``BFGS``
840 The L-BFGS hessian approximation is a low rank approximation to the
841 inverse of the Hessian matrix. The rank of the approximation
843 approximation. Higher the rank, the better is the quality of the
844 approximation. The increase in quality is however is bounded for a
850 2. The Hessian approximation is constrained to be positive
864 step, the initial inverse Hessian approximation is taken to be the
892 parts of the Jacobian approximation which correspond to
1680 and the change in the cost of the linearized approximation.
2148 indicates the rank of the Hessian approximation.