Improving fit of custom function

Question

Romio 2020-8-10

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/577423-improving-fit-of-custom-function

评论： Rena Berman 2020-10-12

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Hello,

I have the following curve.

I want to fit it into a closed-form equation. I tried to use GRABIT to get a vector of values that could plot it.

x = [0.0194119350975558	0.248031785422458	0.291351961297183	0.334455968629621	0.397706884103397	0.439513880182100	0.459876956865727	0.644744294231326	0.658622314646282	0.755249653049490	0.832378588938224	0.889360616685617	0.929005927341429	0.970164417793265	0.990095157392316	1.05248139869694	1.11508380854384	1.20042714903956	1.24439583054116	1.26670442410539	1.33211702500205	1.40033981694848	1.46964345160635	1.56039100565929	1.58464511610412	1.60738604675293	1.67279864764960	1.73734657437711	1.84391766572561	1.92839633205217	1.99143107898366	2.07482890259878	2.26069061525890	2.34387227033173	2.42813476811600	2.53492202800680	2.62113004267167	2.70712188879425	2.73029515652764	2.81693550827709	2.88234810917376	2.98956770614913	3.07491104664485	3.18169830653564	3.28783706079956	3.47910298701692	9.89096458726940]
y = [0.382895015585752	0.936494005646322	0.944570062386241	0.950609811457797	0.946433435220773	0.940255338282152	0.932075520641934	0.473525838625860	0.404256790934756	0.314486318692959	0.241040894764830	0.177811596145283	0.151270422523033	0.138983402579323	0.126730969602380	0.114409362691904	0.104124063449791	0.108058330919451	0.122243310664459	0.132390262039507	0.148576962486111	0.191235662621433	0.244075901098568	0.298917860277301	0.327391580667615	0.341611147379389	0.357797847825993	0.365839317599146	0.369738998102040	0.365528034898250	0.359315350992862	0.344922849447257	0.295740182705652	0.279311373491684	0.273064102619530	0.279000090790788	0.291079588933900	0.301122779408649	0.319414961457149	0.335567074936987	0.351753775383591	0.361762378891574	0.365696646361235	0.371632634532492	0.371459699698661	0.373184724666128	0.372920999044535]

However, I am trying to fit that into an equation, whatever it is. Is that possible? If so, how can I do that

Thanks,

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Walter Roberson 2020-8-12

No, Alex just reported the software he is using when you asked; he did not say it is free.

Alex has posted responses to a number of optimization / fitting questions over the last couple of years, making use of that software to find values. I do sometimes find better values than that software obtains, but the software is producing outputs within a quite small number of minutes, whereas it may take me several hours of work to locate an improved point. For people who do a lot of fitting or optimization, it appears to me that the software he is using is good value for the price. But, Yes, it does cost a fair bit, and Yes, that does effectively act to keep most students from using that other software.

Rena Berman 2020-10-12