# Questions tagged [linear-solver]

Referring to methods for solving linear systems of equations.

273 questions
1k views

### Solving linear systems with ill-conditioned matrices

As per suggestions of the people from MathOverflow, I'm reposting my question here: I'm currently trying to solve a linear system $Ax = B$, where the matrix $A$ is ill conditioned (i.e. nearly ...
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### What strategies / decompositions would be useful to solve the following linear system repeatedly if I only care about time to solution?

Let $A\in \mathbb{R}^{n\times n}$ be symmetric positive semidefinite, and $B\in \mathbb{R}^{n\times n}$ be symmetric positive definite. Suppose $B$ is block diagonal so it is easy to invert. (We ...
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### Construct a preconditioner for the linear system $Ax = b$ from a different matrix

When I use PETSc to solve my linear systems, I always use the subroutine PetscErrorCode KSPSetOperators(KSP ksp,Mat Amat,Mat Pmat) where ...
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### Solve steady state reaction-diffusion/Helmholtz equation numerically

I am solving a problem of the form: $\dfrac{\partial u(x,y,t)}{\partial t} = \nabla^2 u(x,y,t) - f(x,y,t)u(x,y,t) - \kappa(x,y,t)$ At the moment, I am solving this at each time step by assuming a ...
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### How big a matrix can we row reduce in reasonable time?

I have very large matrices that I would like to row reduce (I need to keep track of the steps and find a basis of the kernel/image, not just find the rank). The good news is that I work mod 2 and the ...
511 views

### Solve diffusion equation with linear source term

I would like to solve numerically the diffusion equation, where the sink term depends linearly on the field, and there is field-independent sink: \$\frac{\partial^2 u(x)}{\partial x^2} =f(x)u(x) - \...