Questions tagged [linear-system]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
2answers
197 views

How to verify solution to pre-conditioned linear systems solver?

I am solving Ax=b. A has a very large condition number (> O(10^10)) I am using the conjugate gradients method with point jacobi pre-conditioning. I obtained a solution 'x' that "looks" reasonable. ...
1
vote
0answers
289 views

Why does PETSc take unexpectedly long to set up its KSP solver with a custom preconditioner? [closed]

I am attempting to solve a large system, $\bf{Ax} = \bf{b}$ with the help of PETSc. Due to the size of the problem, I'm using a matrix-free approach, where $\bf{A}$ is just a shell. I'm also providing ...
0
votes
1answer
194 views

Bifurcation of linear PDE

I have a linear elliptic PDE (unfortunately not allowed to be shown here) with a constant parameter $\epsilon$ giving the stable solutions qualitatively shown by the functions below. As we smoothly ...
5
votes
0answers
145 views

Solve ill-posed linear system without transposing matrices?

I am attempting to use an iterative solver to solve $p$ in $$ Jp = -r $$ where $J$ is an $m\times m$ matrix ($m$ is in the order of $10^5$ and never explicitly stored). $J$ is a dense matrix ...
1
vote
0answers
56 views

Integrating the 2d vorticity equation on periodic boundaries

This question is a follow-up of https://stackoverflow.com/questions/44718160/solve-a-linear-system-for-fft-coefficients At some time (kt), the FT of the vorticity (omega) satisfies: ...
0
votes
2answers
125 views

Benefits of matrix multiply over inversion

I have two variations of an iterative algorithm. All the steps of both algorithms are equivalent except one. In this step: Algorithm 1 needs to compute the matrix $ABA^T$ for matrices $A \in \mathbb{...
1
vote
0answers
63 views

FEM/FVM/FD for structural modeling and stability issues due to large structural constants?

I've read that in modeling structures problems, the finite element method (FEM) is typically used. I am unfamiliar with FEM, but I am wondering, in particular, if using FEM, as opposed to finite ...
2
votes
1answer
464 views

Fastest way to solve a sparse unsymmetric system many times

I have to solve a system $Ax^{(n)} = b^{(n)}$ many times, $A$ being a sparse (pentadiagonal in most part of its structure), unsymmetric, constant matrix. Currently, I am performing the LU ...
0
votes
1answer
83 views

MATLAB: Matrix whose elements depend on its indicies

I am trying to put the function $$ f(\mu,\nu) = i^{\nu-\mu} \sum_{0}^{19} H_{\mu-\nu}(7j) + \delta_{\mu,\nu}\ ,$$ $\mu, \nu =-3,-2,...2,3$ into a 7x7 matrix, where $H$ is the Hankel function of the ...
0
votes
1answer
273 views

The system matrix and the right hand side for diffusion equation with staggered grid

In the following staggered grid setting, I want to solve diffusion equation as a linear system. $$\frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}$...
2
votes
1answer
104 views

Solving system of related equations without completely recomputing LU decomposition for each equation

Let $\Sigma$ be positive definite and the $D_i$ positive diagonal. Let the $X_i$ be unknown square matrices. Consider the system of equations: $$(I+\Sigma D_i)X_i=\Sigma\hspace{5mm}\text{for}\...
2
votes
2answers
339 views

Solve a very large linear system (question about a library linear algebra to do this)

I need to solve a very large linear system (coming from finite element method). I'm currently using the Intel MKL library, but the system has been delayed more than 20 hours. The matrix of the system ...
6
votes
2answers
4k views

Solving a system of linear equations with only an approximate solution

I have a system of linear equations that is derived partially from experimental data. Theoretically, the system should have a single, exact solution; however, experimental error causes it to not have ...
3
votes
1answer
584 views

Solve rank one update to LU using plain vanilla LU routine

I have a large number of systems of the form: $$A_ix=b,$$ where each $A_i,i>0$ is a rank one update of $A_{i-1}$ and the $A_i$ are dense matrices. I was wondering whether it is possible to use the ...
-1
votes
1answer
240 views

Solving large system of equations, is linear programming best option? [closed]

I have a problem where I am trying to solve many systems of equations, that have very few variables per equation, but a lot of equations. For example potentially 10 variables max in a single equation,...
3
votes
5answers
1k views

Speed of solving linear system with block diagonal matrix

I have a bunch of 3x3 linear systems of the form $Ax=b$. In general, would it be faster to solve each individual system, or to formulate it as a giant block diagonal system and solve that? I expect ...
8
votes
1answer
432 views

Least-squares for a diagonal matrix

This is a follow-up to a different question I asked with more detail. For $v\in\mathbb{R}^n$, denote $D_v\in\mathbb{R}^n$ as the diagonal matrix with elements in $v$. Given a "tall" matrix $B\in\...
5
votes
2answers
249 views

Solving “Hadamard systems”

Suppose we have two matrices $A$ and $B$ (we can assume they're symmetric; if absolutely necessary I think they may be positive definite). Then, is there any technique for solving $$(A\circ B)x=b,$$ ...
3
votes
1answer
1k views

solving a linearly-constrained sparse linear least-squares problem

[ question reposted from https://math.stackexchange.com/questions/786612/solving-a-linearly-constrained-sparse-linear-least-squares-problem ] Given the system of equations $Ax=b$, subject to $Cx\le ...
5
votes
3answers
345 views

Methods for solving linear systems

This is such a basic topic but there are so many different methods proposed for solving a linear system of equations. I recently found a very good source but couldn't really make sense of all the ...
5
votes
3answers
2k views

What is the best solver for solving a large sparse indefinite system

What's the best solver that can solve a large sparse but indefinite matrix?
2
votes
2answers
1k views

Vortex Panel Method implementation

I'm trying to understand and implement panel methods for a two-dimensional airfoil. I haven't found yet a very detailed explanation on how to implement it, and there are some things I don't' still ...
10
votes
5answers
10k views

Best choice of solver for a large sparse symmetric (but not positive definite) system

I am presently working on solving very large symmetric (but not positive definite) systems, generated by some certain algorithms. These matrices have a nice block sparsity which can be used for ...
12
votes
5answers
2k views

Repeatedly solving $\mathbf{A} \mathbf{x} = \mathbf{b}$ with same $\mathbf{A}$, different $\mathbf{b}$

I am using MATLAB to solve a problem that involves solving $\mathbf{A} \mathbf{x}=\mathbf{b}$ at every timestep, where $\mathbf{b}$ changes with time. Right now, I am accomplishing this using MATLAB'...
5
votes
3answers
352 views

PRIMA gives an unstable result?

I am working with Modified Nodal Admittance representation of circuits. I am doing Model Order Reduction using PRIMA on MATLAB. I am considering these circuits as Descriptor State-Space systems. I ...
11
votes
1answer
901 views

Solving huge dense linear system?

Is there any hope in solving the following linear system efficiently with an iterative method? $A \in \mathbb{R}^{n \times n}, x \in \mathbb{R}^n, b \in \mathbb{R}^n \text{, with } n > 10^6$ $Ax=...
5
votes
2answers
745 views

Largest invertible dense matrix with standard solvers such as Lapack

I have a matrix which is complex symmetric. It is around 50,000 elements per side. It is a Method of Moments matrix. Is it feasible to use a standard direct solver such as Lapack to do a matrix ...

1
2