Kaas. E., B. Sørensen, C. C. Tscherning, M. Veicherts Multi ...
Kaas. E., B. Sørensen, C. C. Tscherning, M. Veicherts Multi ...
Kaas. E., B. Sørensen, C. C. Tscherning, M. Veicherts Multi ...
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{ C } , and s is the variance - covariances<br />
of the errors.<br />
where C = ij + s ij<br />
ij<br />
The estimate of the (M) parameters are obtained by<br />
The error-estimates and error-covariances, eckl are found with:<br />
H<br />
k<br />
T −1<br />
{ COV ( L , L ) } , NxM matrix<br />
= C<br />
k<br />
i<br />
~ T −1 −1 T −1<br />
X = ( A C A + W) ( A C y)<br />
2<br />
X<br />
T −1 −1<br />
m = ( A C A + W)<br />
Appendix B. Cholesky factorisation, generalized.<br />
T<br />
{ ec } = { s<br />
} − H { cov( L , L ) } + H AM ( H A)<br />
kl<br />
kl<br />
Cholesky factorization was originally a procedure to “take the square-root” of a symmetric positive-definite<br />
matrix. However, the equation system described in Appendix A is a combination of a positive definite matrix<br />
and a negative definite one due to the minus sign in eq. (A2). The combined system is illustrated in Fig. B1:
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