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What are some applications of the newton method?

Lipschitz continuity

Stochastic differential equation

Iterative learning control

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The Newton method has various applications across different fields. It can be utilized in iterative learning control (ILC) design for both linear and nonlinear dynamics, allowing for efficient solutions to optimization problems . In the realm of stochastic optimal control, a new iterative method based on the Pontryagin principle extends the Newton method to solve control problems with stochastic coefficients, showcasing global convergence with regression techniques for solving associated equations . Additionally, the Newton-Raphson Method can be employed to approximate areas under curves with high accuracy, offering a new technique for approximating definite integrals under specific conditions, with very small relative errors . Furthermore, iterative methods like the King-like and Jarratt-like families have been developed to solve systems of nonlinear equations and differential equations, providing convergence analysis under general conditions .

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Open access•Journal Article•DOI Perturbed Newton Methods for Solving Nonlinear Equations with Applications Ioannis K. Argyros, Samundra Regmi, Stepan Shakhno, Halyna Yarmola - Show less +3 more 20 Oct 2022-Symmetry 2 Citations	Applications of Newton methods include solving systems of nonlinear equations and differential equations in physical phenomena, particularly in microworlds, where closed-form solutions are challenging to obtain.
Open access•Journal Article•DOI Newton Method for Stochastic Control Problems Emmanuel Gobet, Maxime Grangereau - Show less +1 more 01 Oct 2022-Siam Journal on Control and Optimization 2 Citations	Applications of the Newton method include solving stochastic control problems, such as in the control of batteries providing ancillary services to an electricity network.
Open access•Posted Content•DOI On Some New Applications to Newton-Raphson Method Rachma Merisya Purwatiningsih, Yusuf Muhyiddin, I Putu Eka Wijaya 11 Oct 2022	The Newton-Raphson Method can be applied to approximate areas under curves and definite integrals with low relative error, enhancing accuracy in mathematical calculations.
Other•DOI Newton Method Based ILC 13 Jan 2023	The Newton method is applied in iterative learning control (ILC) design for solving nonlinear optimization problems with input constraints, enhancing efficiency and reliability in various engineering applications.
On Some New Applications to Newton-Raphson Method Treanungkur Mal 11 Oct 2022	The Newton-Raphson Method can be applied to approximate areas under curves and definite integrals with low relative error, as outlined in the paper.

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