Timeline for Writing a function as a sum of functions of bounded diameter
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 12, 2015 at 17:21 | comment | added | The Masked Avenger | Oops. I flipped a sign bit. I no longer know if one-sided functions make sense, much less help with F_D. It might help to dichotomize into x2 bigger or less than D/2, but I am unsure now if that helps. | |
| Jun 12, 2015 at 17:08 | comment | added | The Masked Avenger | Suppose you consider one-sided basic D functions. These are those functions in which x2 and p2 are both positive. Then consider G_D as any function which is a sum of one sided functions. Then f in F_D should be a difference of two functions in G_D. While decomposing f may be hard, dealing with functions in G_D should be easy. Is it? Does it help to decompose f into functions in to F_D' which in turn may be decomposed into functions of G_D for D' bigger than D? | |
| May 22, 2015 at 7:35 | comment | added | The Masked Avenger | Actually, f(x) + f(-x) is in $F_D$, and one can subtract a smaller function g which leaves something not in $F_D$. This reminds me of stacking rectangles, then looking just at the height of the stack as x varies, and using that to reconstruct the rectangles. I suspect you have something similar and NP hard to untangle. | |
| May 22, 2015 at 7:25 | comment | added | The Masked Avenger | It looks like you can drop the alpha's in your definition of $F_D$. Also, all such combinations have domain contained in (-D, D). If a function $f$ majorises a D basic function $g$, hopefully $f-g$ is in $F_D$, which would then lend hope to find quickly a decomposition of $f$. | |
| May 22, 2015 at 7:21 | history | edited | Brendan McKay | CC BY-SA 3.0 |
don't need alpha
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| May 22, 2015 at 6:59 | history | asked | Brendan McKay | CC BY-SA 3.0 |