# Questions tagged [newton-method]

Method for finding successively better approximations to the roots (or zeroes) of a real-valued function

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### Using Newton-Raphson method to solve the hydrostatic equation

I'm trying to use newton-raphson method for nonlinear systems of equations as described in 'Numerical recipies' book in chapter 9.6 to solve the hydrostatic equation for a polytropic star. For each ...
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### Quasi Newton taking very small steps

I have implemented a Quasi-Newton method based on the Hessian approximation. I am noticing that the algorithm takes too many iterations to converge, even though it does converge. What I am not able to ...
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I am trying to solve a problem, which I find quite hard, like, headache-hard. I have to solve the following set of $M$ nonlinear equations: $$F(X)=\begin{bmatrix}f_1 (X)\\f_2 (X)\\...\\f_M (X)\\ \end{... 0answers 67 views ### Mapping to a computationally less expensive basis when employing Newton's method I'm looking for advice, or references, for a change of basis to my dependent variables that leads to a less computationally expensive scheme when solving a system of coupled polynomial equations. ... 0answers 86 views ### Increase convergence of non-linear equations resulting from ODEs I am trying to solve a set of couple ODEs: V_l(r) - r W_l(r) - f1(r) W_l' = 0\tag 1 r^2 h''_l(r) + f2 r h_l'(r) + f3 h_l(r) - f4 U_l(r) = 0 \tag 2 \kappa (U_l + h_l) + V_{l+1} + W_{l+1} = 0\... 1answer 14 views ### How to check curvature of a vector valued function In terms of numerical optimization, the newton-rapson method requires a pos. definite Hessian \nabla^2f respectively pos. curvature for computing the next step p_k by solving$$\nabla^2 f p_k = -\...
When solving time-dependent non-linear equations, such as the non-linear diffusion equation $$\partial_tu=\nabla\left(D(u)\nabla u\right)$$ usually Newton's method is applied, with (coupled with the ...