# Questions tagged [linear-solver]

Referring to methods for solving linear systems of equations.

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### Convergence of Conjugate Gradient Algorithm

I am trying to solve a linear elasticity model using finite element discretization in a rectangle domain [0,1]x[0,1]. For the solution of the the linear system $Ku=F$ I am using the CG algorithm. ...
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### Open-source iterative solvers robust to noise?

I need to solve $Ax=b$ in about 1 million dimensions. Furthermore, A is only accessible through matrix vector products, and these are noisy/inexact. Is there any solver with Python interface I can try ...
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### When is it easy to invert a sparse matrix?

(Crossposted on cstheory.SE) When is it easy to invert a sparse matrix? Specifically, I'm wondering about the cases in which matrix inversion has similar cost to sparse matrix multiplication, hence ...
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### Solving MX=N where M is structured as a Gaussian 4th-moment tensor

I'm looking to solve numerically the following equation for $(d,d)$ variable $X$, in Einstein summation notation $$M_{ijkl}X_{kl}=N_{ij}$$ Where $M$ is a $(d,d,d,d)$ 4th-moment tensor of random ...
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### Is there any function to calculate condition number of sparse matrix in Eigen libraray?

The function JacobiSVD and BDCSVD can calcuate condtion number of a dense matrix via singular values. However I need to know condition number of a sparese matrix due to slow computation speed using ...
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### Testing a block tridiagonal system of equations

In 1D problems, tridiagonal systems of equations are obtained when we use finite-difference or finite-volumes in a structured mesh. A wide solver is the TDMA algorithm here. In two-dimensional ...
46 views

### Nonlinear least squares optimized Jacobian calculation

I have a nonlinear least squares problem, in which I am trying to minimize residuals which can be divided into four classes: $$\min_x ||\epsilon(x)||^2 + ||\xi(x)||^2 + ||\delta(x)||^2 + ||s(x)||^2$$...
159 views