# Tagged Questions

Questions on the algorithmic/computational aspects of linear algebra, including the solution of linear systems, least squares problems, eigenproblems, and other such matters.

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### Robust smoothers for geometric multigrid

I'm searching for robust smoothers for geometric multigrids. By robust I mean: Effective for high order approximations (say spectral element, spectral Discontinuous Galerkin), Parallel (suitable ...
35 views

### Fixing a near singular covariance matrix

Given a near singular covariance matrix, the standard method of 'fixing' it seems to be to add a small damping coefficient $c>0$ to the diagonal, which serves to bump all the eigenvalues up by this ...
18 views

### Algorithm to group Boolean functions by rotation similarity

I'm looking for a way to take the entire vector space of length n Boolean vectors and partition it into vectors that are the same up to a rotation of the entries. For example if n=3 the partitions ...
19 views

### Grouping Boolean vectors by similarity up to a rotation [duplicate]

I'm looking for an algorithm to take the entire vector space of length n Boolean vectors and partition it into vectors that are the same up to a rotation of the entries. For example if n=3 the ...
148 views

### Solving $A=B+AB$ without matrix inverse

I have a linear system of equations that can be expressed $$A=B+AB,$$ where $A$ and $B$ are real, symmetric matrices. I would like to solve for $A$ given $B$. At present, I solve for $A$ directly via ...
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### MCNPX simulation [closed]

I want to ask about neutron source in input file. The problem is I have subcritical core, fuel is mixed between thorium and uranium 50 % and I need to put 2 neutron sources in different places ...
49 views

### Most efficient way to compute eigenvectors / values of this matrix?

I have a symmetric $3 \times 3$ matrix $A$ and I need to compute the eigenvectors and eigenvalues of this. I know that I can use something like Lapack, but I also know that this can be computed ...
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### Probability of reconstructing a word using c substrings from a random sample

Consider a voice recording split into it's phonemes as our sample $S=(s_1,...,s_k) \in \Omega = P^k$. The number of phonemes is $|P| = 40$. Then I have a word $w = (w_1,...,w_n) \in P^n$. I want to ...
48 views

### Numerical Solution of Matrix with Diagonal Elements of Highly Varying Order

I am trying to solve following set of equations: A(i,i-2)*u(i-2) + A(i,i-1)*u(i-1) + (A(i,i)+β(i) )*u(i) + A(i,i+1)*u(i+1) + A(i,i+2)*u(i+2)= B(i) + β(i) where i=1:1000000 If values of β ...
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### Code to update dense QR and Cholesky factorizations

I am looking for some production-ready code to update dense QR and/or Cholesky factorizations (by adding / removing rows and columns or making small-rank updates -- yes, I need all these cases). I ...
96 views

### Advice on handling many “small” matrices in parallel

I'm working on a small fun project on the side for a numerical method I've been working a bit with. Roughly, the computational problem I have to solve is the following: Assume you have a collection of ...
175 views

### Algebraic Multigrid: Why does the product of interpolation and restriction not result in something with norm 1?

I'm currently working with "A Multigrid Tutorial" by Briggs et al, Chapter 8. The construction of the interpolation operator is given as: Then construction of restriction operator and fine grid ...