Timeline for I want a smooth orthogonalization process
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| S Sep 25 at 19:20 | history | suggested | Ryan C | CC BY-SA 4.0 |
minor mathjax clarity changes
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| Sep 25 at 19:10 | review | Suggested edits | |||
| S Sep 25 at 19:20 | |||||
| Sep 25 at 15:20 | history | edited | LSpice | CC BY-SA 4.0 |
Typo
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| Sep 25 at 12:52 | comment | added | Will Sawin | @Jabby If the vectors all have magnitude $\leq B$ and $\geq C$ for constants $B$ and $C$ and determinant $\geq \delta$ then Grahm-Schmidt, and every other orthonormalization procedure, will be uniform continuous in the vectors (because these conditions make the set of bases compact and compactness and continuity imply uniformly continuous). If you want more precise guarantees it may matter which procedure you choose and it depends on if you want abstract continuity or numerical stability (which I am not an expert on). | |
| Sep 25 at 9:22 | comment | added | Jabby | I think my epsilon example may have been misleading. In practice, I don't expect my vectors to be so close to each other. I expect the vectors to be sufficiently large in magnitude and for the angles between all of the vectors to be sufficiently large such that small changes in the vectors produce small changes in the subspace orientation. I'm now wondering if Gram Schmidt is fine if I assume this? Are you able to state what I would have to assume to avoid the problems I am concerned with about Gram Schmit (orthonormal basis vectors discontinuously jumping). | |
| Sep 24 at 23:05 | history | answered | Will Sawin | CC BY-SA 4.0 |