# Tagged Questions

Questions on the various algorithms used in linear algebra computations (matrix computations).

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### Gauss Seidel - Finite Element Method

I am solving an equation using finite element method, and for that I have to use Gauss Seidel to invert a matrix. In Gauss Seidel I am using a "while" which breaks if the absolute error reaches the ...
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Let a set $S=\left\{ {{\mathbf{v}}_{i}}:i\in \mathbb{Z}_{n}^{+} \right\}$, where $\mathbb{Z}_{n}^{+}=\left\{ 1,2,...,n \right\}$ and ${{\mathbf{v}}_{i}}\in {{\mathbb{R}}^{m}}$ for each $i\in \mathbb{Z}... 0answers 25 views ### absolute value matrix and derivation of A^1 b I have a question who could I solve the following sentence? Given is the vector$\vec{b} \in \mathbb{R^n}$and the function$f : GL(n,\mathbb{R}) \to \mathbb{R}^n$with$f(A) = A^{-1}b$. Then ... 0answers 26 views ### Compute the condition number of the matrix and show for what$\Delta x$it is singular Given the laplacian$N \times Nmatrix \begin{align*} A=\frac{1}{(\Delta x)^2}\begin{pmatrix} 2&-1& & &\\ -1&2&-1& &\\ &\ddots&\ddots&\ddots&\\ &... 0answers 13 views ### Determinants using Row Reduction replacement I am aware replacement does not affect the value of determinant when doing a row reduction. However, I realised there isn't a good explanation on how to handle different forms of replacement when ... 0answers 22 views ### Given a triangular matrixT$, can we find an upper bound for$\| |T^{-1}||T|\|$? Given a triangular matrix$T$, can we find an upper bound for$\| |T^{-1}||T|\|$, where$|T| =|[T_{ij}]| = [|T_{ij}|]$? 0answers 12 views ### Error estimate in iterative refinement for solving a linear system The iterative refinement can be illustrated as follows: given an approximate solution$\hat{x}$of the system$Ax = b$, at the$n^{th}$step of the refinement,$r = b- A\hat{x}^{(n)}$, Solve$Ad^{(n)...
Modified Gram-Schmidt is known to be numerically less stable than methods like Householder orthogonalization and also not quite as fast at approximately $2mn^2$ flops. So in practice do we ever use it,...