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我正在使用 cftool 自定义拟合 Mössbauer 光谱数据。有两个系数，Gamma 和 N0。

N = f(v)
  = (299792458000^2*Gamma^2*N0)/(299792458000^2*Gamma^2+4*v^2*(4.29383292e-15)^2)

使用默认设置（信任区域、健壮关闭等）我得到以下拟合：

Fit computation did not converge:
Fitting stopped because the number of iterations or function evaluations exceeded the specified maximum.

Fit found when optimization terminated:

General model:
     f(v) = (299792458000^2*Gamma^2*N0)/(299792458000^2*Gamma^2+4*v^2*(4.29383292e-
                    15)^2)
Coefficients (with 95% confidence bounds):
       Gamma =      0.9137  (-Inf, Inf)
       N0 =   2.454e+04  (2.059e+04, 2.849e+04)

Goodness of fit:
  SSE: 6.41e+11
  R-square: -2068
  Adjusted R-square: -2073
  RMSE: 4.013e+04

Warning: A negative R-square is possible if the model does not contain a constant term and the fit is poor (worse than just fitting the mean). Try changing the model or using a different StartPoint.

如果我切换到 Levenberg-Marquardt，我会通过数据得到一条直线：

General model:
     f(v) = (299792458000^2*Gamma^2*N0)/(299792458000^2*Gamma^2+4*v^2*(4.29383292e-
                    15)^2)
Coefficients (with 95% confidence bounds):
       Gamma =       0.793  (-Inf, Inf)
       N0 =   6.456e+04  (6.447e+04, 6.465e+04)

Goodness of fit:
  SSE: 3.098e+08
  R-square: 2.22e-16
  Adjusted R-square: -0.002513
  RMSE: 882.3

在此处输入图像描述

为什么这两种情况都如此糟糕？

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1 回答 1

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f(v) 简化为，f(v)=N0/(1+(2.8645e-26*(v/Gamma))^2)因此分母中的 1 占主导地位，直到 (v/Gamma) 开始变得像 10^25 一样大。使用 0.793 的 Gamma 和 |15| 的 v 我认为matlab可能很难收敛到N0以外的任何东西

于 2013-01-20T19:01:53.273 回答