A popular krylov subspace method for solving linear systems of equations, particularly those that exhibit symmetric positive definiteness.

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### Flexible Conjugate Residual

If we want to use variable preconditioning in Conjugate Gradient, we can replace the Fletcher–Reeves by the Polak–Ribière formula (https://en.wikipedia.org/wiki/Conjugate_gradient_method#...
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### Bachelor thesis going out of hand, need help [closed]

I am currently working on my bachelor thesis, which aims to enhance the multigrid preconditioned conjugate gradient algorithm proposed by Tatebe in 1993 using Deep Learning. Currently, I am ...
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• 3,136
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### 2-norm of solution update suddenly becomes zero after a few iterations

I am trying to solve the Poisson equation in 2D for heterostructure devices. I have linearized the equation and discretized it using FDM. I am using BiCGStab to iteratively solve for the solution as ...
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### Why does smoothed aggregation multigrid method used as preconditioner in conjugate gradient slows down the solution time?

I'm solving a system of linear equations obtained from the FEM discretization of a simple linear elasticity problem on a cube with zero displacements at one plane and a load on the opposite one. The ...
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### What happens when I use a conjugate gradient solver with a symmetric positive semi-definite matrix?

I have a symmetric positive semi-definite matrix, i.e., a laplacian and wonder what may happen when I use a CG solver, that is an algorithm for positive definite matrices. What happens when the ...
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### Conjugate Gradient for nonlinear equation system

Is it possible to apply adaptions of the conjugate gradient algorithm i.e. Fletcher-Reeves, Polak-Ribere or others to systems of nonlinear equations? How should the equation system be adjusted so one ...
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### Arnoldi Decomposition Algorithm

I try to get into GMRES via Arnoldi-Decomposition. For my understanding, I Implemented the Arnoldi-Decomposition in python. ...
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### In which cases does the nonlinear conjugate gradient method take more than $n$ steps?

I have programmed a couple of Matlab implementations of nonlinear Conjugate Gradient methods (Fletcher Reeves and Polak Ribeire). However, I am concerned with how many steps it's taking to optimise ...
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### Explanation of subspace strategy regarding CG described in Golub's book

I was wondering about the last paragraph in Matrix Computations (4th edition) by Golub, Chapter 11 (11.3.3), specifically his explanation of subspace strategy for Conjugate Gradient. Note that in ...
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