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  2. Nonlinear conjugate gradient method - Wikipedia

    en.wikipedia.org/wiki/Nonlinear_conjugate...

    Whereas linear conjugate gradient seeks a solution to the linear equation =, the nonlinear conjugate gradient method is generally used to find the local minimum of a nonlinear function using its gradient alone. It works when the function is approximately quadratic near the minimum, which is the case when the function is twice differentiable at ...

  3. 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 ...

  4. Nonlinear system - Wikipedia

    en.wikipedia.org/wiki/Nonlinear_system

    In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]

  5. List of numerical libraries - Wikipedia

    en.wikipedia.org/wiki/List_of_numerical_libraries

    Lis is a scalable parallel library for solving systems of linear equations and eigenvalue problems using iterative methods. MINPACK is a library of FORTRAN subroutines for the solving of systems of nonlinear equations, or the least squares minimization of the residual of a set of linear or nonlinear equations.

  6. Iterative method - Wikipedia

    en.wikipedia.org/wiki/Iterative_method

    In the absence of rounding errors, direct methods would deliver an exact solution (for example, solving a linear system of equations = by Gaussian elimination). Iterative methods are often the only choice for nonlinear equations. However, iterative methods are often useful even for linear problems involving many variables (sometimes on the ...

  7. Linear dynamical system - Wikipedia

    en.wikipedia.org/wiki/Linear_dynamical_system

    Linear dynamical systems can be solved exactly, in contrast to most nonlinear ones. Occasionally, a nonlinear system can be solved exactly by a change of variables to a linear system. Moreover, the solutions of (almost) any nonlinear system can be well-approximated by an equivalent linear system near its fixed points. Hence, understanding ...

  8. Numerical continuation - Wikipedia

    en.wikipedia.org/wiki/Numerical_continuation

    Numerical continuation is a method of computing approximate solutions of a system of parameterized nonlinear equations, (,) = [1]The parameter is usually a real scalar and the solution is an n-vector.

  9. Nonlinear system identification - Wikipedia

    en.wikipedia.org/wiki/Nonlinear_system...

    The applications of system identification include any system where the inputs and outputs can be measured and include industrial processes, control systems, economic data, biology and the life sciences, medicine, social systems and many more. A nonlinear system is defined as any system that is not linear, that is any system that does not ...

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