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Questions tagged [numerical-linear-algebra]

{numerical-linear-algebra} questions involving algorithms for linear algebra computations.

The {numerical-linear-algebra} tag is for questions dealing with algorithms for linear algebra computations. Common problems include decompositions (eg., LU, QR, SVD), eigenvalues computation, and Gaussian elimination. The computer libraries BLAS and LAPACK implement basic algorithms for numerical linear algebra computation.

290 questions
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How do I find elements of an algebra which generate an algebra contained in a fixed subspace?

Suppose $V$ is a linear subspace of a finite dimensional $C^*$-algebra $A$. (Feel free to assume $A$ is a multi-matrix algebra over $\mathbb C$.) I would like to find $x \in V$ such that $\mathbb C [x] \subset V$ (that is, the algebra generated by…
Scott Morrison
  • 7,540
2
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1 answer

Where has the necessary and sufficient condition for the convergence of the unshifted QR algorithm been stated?

I've obtained a necessary and sufficient condition for the unshifted QR algorithm to converge. The condition for the algorithm to converge for a square matrix $M$ is: For any two eigenvalues $\lambda$ and $\mu$ of $M$, if $|\lambda| = |\mu|$ then…
wlad
  • 4,823
1
vote
1 answer

Can the condition number of a Jordan basis be made stubbornly large?

For each $k \in \mathbb R$, does there exist a non-empty open ball $B$ of $\mathbb R^{2 \times 2}$ such that for all $M \in B$ and Jordan decompositions $PJP^{-1}$ of $M$, the condition number $\kappa(P)$ is greater than $k$? The condition number of…
wlad
  • 4,823
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L1 Norm regression

First time poster...apologies for formatting. I am trying to devise a solution to a familiar linear algebra equation, Ax=b, where all elements in A are non-negative and all the elements in b are positive. My constraint is that the difference between…
Jason
  • 11
1
vote
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Why de-blurring a blurred image is an ill-conditioned problem?

Why de-blurring a blurred image is an ill-conditioned problem? What's the intuitive explanation? How to show it using the condition number?
dxdydz
  • 139
0
votes
1 answer

Need help with computational and numerical methods for solve equations

This is my first question on this community. I am a applied scientist, not a mathematician. I have the following simplified problem: Let $u: [0,1] \rightarrow \mathbb{R}_+$ a real valued function and $k\in \mathbb{R}$. The function $u(\cdot)$ is…
fnd
  • 3