# Questions tagged [newton-method]

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

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### How to use Newton-Raphson method to handle nonlinear terms in coupled system of PDEs?

I'm trying to solve the Nonlinear Schrodinger's Equation (NLSE) in 2D using Finite Elements, but I don't know how to handle the nonlinear term. I suppose I have to apply the Newton-Raphson algortihm ...
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### How to the determine the initial conditions of the following coupled non-linear ODEs

I am trying to determine the roots (initial conditions) of $θ'$ and $f''$ in the set of ODEs below so I can solve as an initial value problem using the Runge-Kutta method. I tried using Newton-Raphson ...
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### How to calculate/derive analytic FEM Newton Jacobian

I trying to wrap my head of derivation of the analytic FEM Jacobian for the Newton method. Say we have a nonlinear Poisson problem of the (weak) form $$\int a(u)\nabla\ u\cdot \nabla v = \int f v$$ ...
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### How to use Wolfe-Powell step-size control in quasi-Newton method?

I'm trying to find the minimum of a function using the quasi-Newton method with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. But I want to change the following implementation, so that: 1) ...
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### GMRES vs Newton-GMRES for Solving nonlinear PDE's

Often when numerically solving nonlinear PDE's using method of lines approach with an implicit integrator a system of nonlinear equations have to be solved. To be more specific, let's say we have ...
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### Inverse kinematics BFGS divergence

I am trying to implement inverse kinematics solver using BFGS as stated in the paper Xia2017. In the test experiment, i created 4 objects in 3-dimensional space: Node, Node1, Node2, Node3. Each Node ...
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### Finding null vectors of a parameter-dependent matrix

I have dense complex matrices $M(z)$ in which each element $M_{ij} = M_{ij}(z)$ depends on a complex parameter $z$. I need to find $z$ such that the matrix $M$ gets singular, i.e. I am looking for ...
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### Defining a condition number and termination criteria for Newton's method

The condition number of function evaluation $$\mathrm{cond}(f,x) := \left| \frac{x f'(x)}{f(x)} \right|$$ is infinite at a root of $f$. Hence it is useless for rescaling a tolerance which defines an ...