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  2. 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.

  3. Matrix-free methods - Wikipedia

    en.wikipedia.org/wiki/Matrix-free_methods

    It is generally used in solving non-linear equations like Euler's equations in computational fluid dynamics. Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver. [7] Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage. To ...

  4. 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 ...

  5. Homotopy analysis method - Wikipedia

    en.wikipedia.org/wiki/Homotopy_analysis_method

    The homotopy analysis method is also able to combine with other techniques employed in nonlinear differential equations such as spectral methods [7] and Padé approximants. It may further be combined with computational methods, such as the boundary element method to allow the linear method to solve

  6. 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 ...

  7. Levenberg–Marquardt algorithm - Wikipedia

    en.wikipedia.org/wiki/Levenberg–Marquardt...

    The primary application of the Levenberg–Marquardt algorithm is in the least-squares curve fitting problem: given a set of empirical pairs (,) of independent and dependent variables, find the parameters ⁠ ⁠ of the model curve (,) so that the sum of the squares of the deviations () is minimized:

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