# Tag Info

Accepted

### What is this regularization technique?

All they are doing is taking the problem of minimizing $x^T x$ subject to $A x = b$ and then forming a Lagrangian, like so: $$L(x, \lambda) = x^T x + \lambda^T (A x - b)$$ From here, you want to find ...
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### What is this regularization technique?

I have never seen it used for underdetermined systems, but for overdetermined systems (tall thin $A$) the version obtained replacing $A$ with $A^T$ in your block matrix a common reformulation, known ...
• 11.3k
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### Solving $(I-Q)x={\bf 1}$ for sub-stochastic sparse $Q$ of dimension 5M $\times$ 5M

Yea, iterative solvers are often more effective for sparse problems, as long as the condition number isn't too large. IterativeSolvers.jl provides several common methods. The general recommendation ...

### What is this regularization technique?

Spektr's answer is already great but note that you can also argue about this in the following manner $2x + A^T \tau = 0$ and $Ax=b$ implies that $x = -\frac{1}{2} A^T\tau$ and plugging it in the ...
• 2,112
Accepted

### Implementing matrix term version of Gauss-seidel

The $L$ and $U$ of Gauss-Seidel are different from the $L$ and $U$ that come from the LU factorization. For Gauss-Seidel, $L$ and $U$ are what you get if you zero out the upper or lower part, ...
In the Gauss iterative method (Gauss-seidel) we decompose the linear system $Ax=b$ into $x^{k+1} = (L+U)^{-1}(b-Ux^{k})$ as exposed in the reference indicated (Scientific Computing An Introductory ...
A partial answer to your point 2, from a comment I wrote to a now-deleted answer: there is nothing wrong about $\det A_j$ being very small: determinants are notoriously poorly scaled. For instance the ...