added html files

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mhjensen
2018-08-24 06:35:38 +02:00
parent 3a6bdf1450
commit dc7ce90ee7
20 changed files with 159 additions and 2504 deletions
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@@ -393,9 +393,10 @@ and
!bblock
For a linear fit we don't need to invert a matrix!!
Defining
!bt
\[
\gamma = \sum_{i=0}^{n-1}\frac{n-1}{\sigma_i^2},
\gamma = \sum_{i=0}^{n-1}\frac{1}{\sigma_i^2},
\]
!et
@@ -419,7 +420,7 @@ For a linear fit we don't need to invert a matrix!!
\gamma_{xy} = \sum_{i=0}^{n-1}\frac{y_ix_{i}}{\sigma_i^2},
\]
!et
and show that
we obtain
!bt
\[
\beta_0 = \frac{\gamma_{xx}\gamma_y-\gamma_x\gamma_y}{\gamma\gamma_{xx}-\gamma_x^2},
@@ -431,7 +432,7 @@ and show that
\]
!et
The LSM suffers often from both being underdetermined and overdetermined in the unknown coefficients $\beta_i$. A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
This approach (different linear and non-linear regression) suffers often from both being underdetermined and overdetermined in the unknown coefficients $\beta_i$. A better approach is to use the Singular Value Decomposition (SVD) method discussed below. Or using Lasso and Ridge regression. See below.
!eblock