# Tagged Questions

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### Efficient methods to solve large dense singular least square problem (linear system)

I am trying to solve a singular linear least square problem: $$minimize: \phantom{2} ||Ax-b||^2 \\ subject \phantom{2} to: \phantom{2} x \ge 0$$ Here $A \in R^{n \times m}$, and $n\lt m$. here m ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Block preconditioners and condition number

I am working with block Jacobi like preconditioners which are very cheap for my problem. But I could not find much about the dynamics of basic preconditioners (block Jacobi, Gauss-Seidel, ILU etc). ...
276 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 ...
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### Get symmetric Finite Difference matrix in non Laplacian settings

I would like to solve a system of differential equations $u+\nabla(\nabla\cdot u)=f$ or in more detail $a+\partial_t^2a+\partial_t\partial_xb+\partial_t\partial_yc=f$ ...
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### 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 ...
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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 $$(A\circ B)x=b,$$ ...