Timeline for Speed of convergence of vector expansions in non orthogonal basis
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2014 at 5:04 | comment | added | Kevin Ventullo | Hmm, yeah that was nonsense. Not sure what I was thinking | |
| Jun 18, 2014 at 22:18 | comment | added | fedja | @Kevin Ventullo I guess I know how to derive a few things like Riemann Hypothesis (or its negation, if you prefer) from the inequality you wrote (the most likely reason is, of course, that you meant something completely different and your fingers just slipped on the keypad when typing :-)) | |
| Jun 18, 2014 at 12:43 | comment | added | timur | If the dimension of the Hilbert space is infinite, you can find a vector whose expansion converges with the error going to $0$ slower than any prescribed function that goes to $0$, even in the orthogonal basis setting. However, useful things can be said depending on the particular situation. For example, if your space $X$ is $L^2$, and the basis elements $V_k$ are some kind of piecewise polynomials, then the convergence is faster for smoother functions. | |
| Jun 18, 2014 at 8:41 | comment | added | Yuriy M | well ok, this assumes we know $a_k$, but the situation we have is that we have $X$ and $\{V_k\}$. Since in nonorthogonal case finding $a_k$'s requires solving a system of general linear equation, we can't get much information about the behavior of $a_k$. Perhaps I should have said, are there any known results about convergence that rely on the properties of $X$ and $\{V_k\}$. | |
| Jun 18, 2014 at 8:18 | review | First posts | |||
| Jun 18, 2014 at 8:26 | |||||
| S Jun 18, 2014 at 8:18 | history | suggested | Loïc Teyssier | CC BY-SA 3.0 |
Latexed and removed non-relevant introductory sentence
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| Jun 18, 2014 at 8:14 | review | Suggested edits | |||
| S Jun 18, 2014 at 8:18 | |||||
| S Jun 18, 2014 at 8:13 | history | suggested | leo monsaingeon | CC BY-SA 3.0 |
LaTeX formatting fixed
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| Jun 18, 2014 at 8:08 | review | Suggested edits | |||
| S Jun 18, 2014 at 8:13 | |||||
| Jun 18, 2014 at 8:07 | comment | added | leo monsaingeon | You may want to use LaTeX formatting (just use the usual $symbols) for a better diplay next time... | |
| Jun 18, 2014 at 8:00 | history | asked | Yuriy M | CC BY-SA 3.0 |