# Questions tagged [linear-solver]

Referring to methods for solving linear systems of equations.

273 questions
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### Is it possible to output the matrix condition number from pardiso (MKL)? [closed]

I am assuming the pardiso solver calculates (or estimates) the condition number before proceeding to the solution phase. Is there a way to make pardiso output the condition number? Alternatively, ...
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### Solving linear system with 6 equations and 22 unknowns for six of the unknowns

I am trying to find the solution for the M variables in the following system. 0 = C_{b} M^{b}_{x} - M^{a}_{x} k_{2a} + M^{a}_{y} \left(\omega - \omega_{a}\right)\\ 0 = C_{a} M^{a}_{x}...
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### External solver in Abaqus/Ansys

Is it possible to call an external linear solver from Abaqus and/or Ansys? This solver (which is supplied by me) would get the sparse matrix A and the right hand side vector b as inputs, and would ...
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### preconditioning a krylov method with another krylov method

In method like gmres or bicgstab it could be attractive to use another krylov method as a preconditioner. After all they are easy to implement in a matrix-free way and in a parallel environment. For ...
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### Surface normals integration

I am trying to reconstruct a 3D surface given the normals of the unknown surface. Reading through this paper on section 4 they say [...] denote the surface by $z(x,y)$. The directions of the ...
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### GPU-accelerated libraries for solving sparse linear systems

There are several libraries to (iteratively) solve large sparse linear equation systems in parallel on a number of CPUs. Our parallel cluster also has attached powerful GPUs, but so far, I did not ...
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### Do black-box preconditioners for matrix-free methods exist?

Jacobian-Free Newton-Krylov (JFNK) methods, and Krylov methods in general, can be very useful because they don't require explicit storage or construction of a matrix, only the results of matrix-vector ...
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### Does length unit in FEM affect numerical condition?

I try to solve a system of coupled PDEs using FEM. Unfortunately, the originating matrix has very poor condition. After days of double checking and thinking, I suspect the following reason: Given a ...
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### Linear equation system: Direct solver works, iterative solver does not

I have to solve for x in b = A*x, where a is sparse. This works fine with Matlab's mldivide: x = A \ b. Since I will have to use an iterative algorithm for very large A, I'm currently testing Matlab's ...
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### Solver library for matrix-free linear equation system

I will have to solve a large linear system. I'm now looking for a solver that works "matrix-free" (So that I just have to specify a matrix-vector product, but not the matrix). As far as I understand (...
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### Is the Thomas algorithm the fastest way to solve a symmetric diagonally dominant sparse tridiagonal linear system

I am wondering if the Thomas algorithm is the fastest way (provably?) to solve a symmetric diagonally dominate sparse tridiagonal system in terms of algorithmic complexity (not looking for ...
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### Large binary programming problem

I have 10000 variables (each of them is binary), vector of positive coefficients and a matrix $A$ ($10000\times10000$), if $A_{ij}=1$, then $i$th and $j$th variables can take 1 simultaneously, if it ...
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### Least squares fitting

I have the following equation I came across which was solved using least squares $x = \sum_{n=1}^{N} A_{n} y_{n}$ Where $x$ is a $m \times p$ matrix and $y$ would be of size $m \times p$ as well ,...
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### Solving system of linear equations with cyclic tridiagonal matrix

I have this problem in my textbook: Suggest efficient algorithm for solving system of linear equations with cyclic three-diagonal matrix, that is of the form: \begin{bmatrix} a_1&b_1&0&...
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### Sparse linear solvers in C?

I'm working on translating a discontinuous Galerkin code from MATLAB to C and I'm at the final point where I need to solve a sparse system. I've taken a course in C before but I'm very rusty and wasn'...
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### Would recalculating the residual in the conjugate gradient method help?

The conjugate gradient method suffers from an accumulation of errors as it continues. For this reason it is unwise to use it as a direct solver. My question is, would it help to recalculate the ...
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### Determine the step size in a differential equation numerical solver

How can we define the precision we require in a numerical differential equation solver? What is it that I have to optimize to know? And how do I know that I'm at a sufficient time-step value? For ...