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2. Newton–Krylov method - Wikipedia

   en.wikipedia.org/wiki/Newton–Krylov_method

   Newton–Krylov methods are numerical methods for solving non-linear problems using Krylov subspace linear solvers. [1] [2] Generalising the Newton method to systems of multiple variables, the iteration formula includes a Jacobian matrix. Solving this directly would involve calculation of the Jacobian's inverse, when the Jacobian matrix itself ...

3. Quasilinearization - Wikipedia

   en.wikipedia.org/wiki/Quasilinearization

   In mathematics, quasilinearization is a technique which replaces a nonlinear differential equation or operator equation (or system of such equations) with a sequence of linear problems, which are presumed to be easier, and whose solutions approximate the solution of the original nonlinear problem with increasing accuracy.

4. Newton's method - Wikipedia

   en.wikipedia.org/wiki/Newton's_method

   This allowed him to derive a reusable iterative expression for each problem. Finally, in 1740, Thomas Simpson described Newton's method as an iterative method for solving general nonlinear equations using calculus, essentially giving the description above. In the same publication, Simpson also gives the generalization to systems of two ...

5. Nelder–Mead method - Wikipedia

   en.wikipedia.org/wiki/Nelder–Mead_method

   It is a direct search method (based on function comparison) and is often applied to nonlinear optimization problems for which derivatives may not be known. However, the Nelder–Mead technique is a heuristic search method that can converge to non-stationary points [ 1 ] on problems that can be solved by alternative methods.

6. Relaxation (iterative method) - Wikipedia

   en.wikipedia.org/wiki/Relaxation_(iterative_method)

   [5] [6] [7] They have also been developed for solving nonlinear systems of equations. [1] Relaxation methods are important especially in the solution of linear systems used to model elliptic partial differential equations, such as Laplace's equation and its generalization, Poisson's equation. These equations describe boundary-value problems, in ...

7. Powell's dog leg method - Wikipedia

   en.wikipedia.org/wiki/Powell's_dog_leg_method

   Powell's dog leg method, also called Powell's hybrid method, is an iterative optimisation algorithm for the solution of non-linear least squares problems, introduced in 1970 by Michael J. D. Powell. [1] Similarly to the Levenberg–Marquardt algorithm, it combines the Gauss–Newton algorithm with gradient descent, but it uses an explicit trust ...