Questions tagged [iterative-method]

Question 1

I have a fairly general question, which I don't think depend a lot on my particular application. Consider a linear system $Ax = b$ that I would like to solve with preconditioned MinRes. Call the ...

Question 2

I was numerically solving ordinary differential equations and I encountered some very interesting properties. The forward Euler method for a simple harmonic oscillator diverges, it has energy drift ...

Question 3

I've been working on a simple multigrid solver that uses Jacobi iterations to solve the Poisson equation as a little exercise. What I'm finding, however is that my solver doesn't seem to converge, or ...

Question 4

For large positive definite matrices $A$, conjugate gradients is the method of choice for solving linear systems $$Ax=b.$$ Convergence of conjugate gradients heavily relies on having a good ...

Question 5

In Constantine A. Balanis' book about antennas, he introduced the method of moments for current distribution over a finite dipole. I found that the method of moments works very bad for a half-...

Question 6

I am working on evaluating the integral: $ I(\vec{r}) = \int f(k) e^{i\vec{k} \cdot \vec{r}} d\vec{k}, $ for a system with a tight-binding dispersion relation given by: $ \epsilon_k = -2t \left[\cos(...

Question 7

I have a question regarding the computational complexity of the ILU preconditioner in Python. I am trying to implement an ILU(0) preconditioner using the following code: ILUfact = sla.spilu(...

Question 8

The simplest possible matrix I can think of to use an arnoldi method is the identity matrix. In this case the Krylov sequence is just $\{v, v, v, v, \cdots\}$ for any $v$. Thus the span of the krylov ...

Question 9

I am interested in analyzing convergence of the Jacobi method to solve the linear system $Ax=b$, $$\begin{pmatrix} 2 & 4 \\ 1 & 1 \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \end{pmatrix} = \...

Question 10

In my case, I am solving $AX=B$ repeatedly, but the solution usually doesn't change much. So it'd probably be faster than me when I start from the previous solution and iterative, rather than solving ...

Question 11

How can I define preconditioners (SPILU, SPAI, etc.) for sparse iterative methods (TFQMR, GMRES, CGS, etc.) for the matrix-free left-hand side? I defined $Ax=b$ using matrix-free $A$ (with ...

Question 12

I have been using recently AMG as preconditioner for CG with several meshes for simple elliptic problems discretised with linear elements on "complicated" three dimensional geometries and I ...

Question 13

I am looking for an Iterative Numerical PDE solver for 1D Burgers equation. I need to have access to the intermediate solutions of the Numerical Solver. By iterative methods, I mean techniques which ...

Question 14

Problem: I want to solve the eigenvalue problem $$x=Ax$$ to the eigenvalue $1$ for a large matrix (roughly $N^3\times N^3$ and $N$ ranges from 10 to 100) where $A$ is stochastic (i.e. all entries are ...

Question 15

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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Questions tagged [iterative-method]

Solving linear systems with a clustered spectrum except for 1 eigenvalue

Euler method and energy drift for a simple harmonic oscillator

Multigrid with Jacobi iteration seems to converge wrong

Generalizable Preconditioners for Solving Linear Equations with Positive Definite Matrices. $Ax=b$

Why does MOM fail for large number of subdivision for finite dipole?

How to Integrate in Energy Domain for a Tight-Binding System?

ILU Preconditiner Implementation in Python

How does the Arnoldi iterations algorithm deal with repeated eigenvalues?

Diagonal and Upper-Triangular pre-conditioning for Jacobi

Efficient Solver for Solving a Large Linear System Sequentially of a Positive Definite Matrix

Preconditioner Implementation with matrix-free methods (sparse iterative solvers)

Computational efficiency of Galerkin projection in AMG

Iterative PDE solver for 1D Burgers equation

Is there a fast matrix-free inverse power iteration?

Flexible Conjugate Residual

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