# Tagged Questions

Referring to sparse matrices with concentrations of non-zero elements along a combination of diagonals, subdiagonals, and/or superdiagonals.

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### Solve for $C$ such that $C^{T}AC$ is banded of given width

Given a symmetric matrix $A$, the Lanczos algorithm outputs $C$ such that $C^{T}AC$ is tridiagonal. Is there a generalization of this such that $C^{T}AC$ is banded of specific width $w$? Note that $C$...
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### solving tridiagonal system with multiple right hand sides

I need to solve a tridiagonal system (positive definite, diagonally dominant) $Ax = b$ in a time stepping loop. $A \in \mathbb{R}^{N \times N}$ remains constant but $b$ changes during each time ...
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### Writing the Poisson equation finite-difference matrix with Neumann boundary conditions

I am interested in solving the Poisson equation using the finite-difference approach. I would like to better understand how to write the matrix equation with Neumann boundary conditions. Would someone ...
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### How should I build a 2D 5-point stencil Laplacian matrix in parallel?

I'm making a simple eigenvalue solver with SLEPc, using a 5-point stencil and the finite difference method. I want to be able to assemble the matrix in parallel. My first thought was just to use <...
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### How does LAPACK solve tridiagonal systems and why

In my project I have to solve a couple of tridiagonal matrices at every time step, so it is crucial to have a good solver for those. I did my own implementation, just the classical way to do it ...
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### What heuristics can be used to minimize the asymptotic matrix bandwidth of a 5-point Laplacian discretization?

I can see that there are multiple heuristics to achieve a matrix with minimum bandwidth. As heuristics, they can't guarantee an optimal solution in polynomial time (after all, the problem is NP-...