# Questions tagged [newton-method]

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

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### Strong coupling of a non-linear multiphysic problem: failure with Newton Raphson method

I am trying to solve a multiphysic problem using finite elements and a Newton Raphson solution scheme. I have two non-linear subsystems that are coupled bi-directionally. The first subsystem includes ...
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### Optimization based integration for MPM

I'm considering implementing (just for simplicity) the unconstrained implicit optimization based integration for Material Point Method as described in Chenfanfu Jiang's thesis on MPM (the minimization ...
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### Does applying the Newton-Raphson iteration for matrix reciprocal refine a matrix inverse from LU/GE?

This is a follow-up to this answer. Suppose you have a possibly very ill-conditioned matrix $A$, and you compute its inverse with LU/GE to get $X_{\text{lu}}\approx A^{-1}$. The Newton-Raphson ...
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### What would be a good approach to solving this large data non-linear least squares optimisation

Introduction to Problem I'm using a Truncated Signed Distance Function to perform 3D reconstruction from depth images. Essentially I have a large voxel grid where each voxel contains the signed ...
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I have read this and other threads on this site on BFGS, but I still don't have a clear understanding of what it's meant by low-rank updates. For example, I read the following in this book: The ...
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### Doubt regarding principled approach towards approximating the Hessian

In my optimization problem, the hessian has a structure such that it can be written as the sum of two matrices. Populating the first of the matrices is efficient. Populating the second one is ...
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### Eigenvalues of $ab^T$

In deriving a Newton scheme, I end up with a Jacobian matrix of the form $J=I+ab^T$ where $a,b$ are vectors. For practical reasons, I want to approximate it by a symmetric positive definite matrix. ...
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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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### Are there special methods for solving $f'(z)=0$ for analytic $f$?

I am trying to solve a bunch of equations for the zeros of the derivative of an analytic function, and I would like to know if there exist methods that exploit this structure to provide better ...
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### The linear system in Quasi Newton method

I have implemented a Quasi Newton method for my problem, where I use the Hessian matrix approximation based approach. Hence, there is a linear system solve in every iteration. I solve the linear ...
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### Solving a large system of nonlinear equations, where timeseries are the unknown

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{...
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### How to implement Newton method in solving 1D PDE system? (ie. Poisson eq, continuity eq, drift-diffusion eq.)

I want to solve PDE system, which consists of Poisson equation, continuity equations for electron and hole with drift-diffusion equation numerically, by using method called Newton's method. This ...
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### Why do Newton-Krylov iterations stagnate in this problem? [closed]

Consider this integro-differential heat equation taken from SciPy documentation page: $\nabla^2 P = \alpha \left(\iint_\Omega \cosh(P)dx dy \right)^2$ which was found in this question. In the ...