Timeline for methods for interpolating a function, holomorphic in the upper halfplane
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Jul 19 at 7:46 | comment | added | David Roberts♦ |
Fiktor's links are really long urls, and the goo.gl link shortner is going away, so here is the first link drive.google.com/file/d/…, and the other two are broken.
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| Oct 19, 2010 at 12:58 | vote | accept | Fiktor | ||
| Oct 19, 2010 at 12:58 | history | bounty ended | Fiktor | ||
| Oct 19, 2010 at 12:56 | comment | added | Fiktor | I hoped for better results, but nevertheless your method works (number of (real) coefficients = 25--50% of the (total) number of data points). Some tests are in this Mathematica 7.0 file: goo.gl/65Bt. I've done a computational experiment: I've taken a function, data points from it (I've added small noise), and interpolated it by these points, using your method. On the following images dotted line is initial function. Re: goo.gl/2IQK, Im: goo.gl/vFPW. Often coefficients do not obey inequalities, so I am constraining them. Thank you for your answer. | |
| Oct 17, 2010 at 7:07 | comment | added | Greg Kuperberg | But, without the linear constraints, it's just Lagrange interpolation. Maybe allowing a huge number of terms in the fit will lead to trouble even with the inequalities, I'm not sure. | |
| Oct 17, 2010 at 5:32 | comment | added | Dylan Thurston | Concretely, Greg's suggestion amounts to fitting your original function $N(x)$ by $\sum_{k\ge 0} a_k \left(\frac{i-z}{i+z}\right)^k$. I might try doing this naively first, and hoping that the additional convex constraints are satisfied automatically. | |
| Oct 16, 2010 at 19:50 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |