Jacobian changes with iterations

With the Jacobian X prepared as indicated and the vector of variables p limited to the independent coordinates, X has maximum rank and the problem can be solved by the iterated least-squares treatment. After each iteration step, p should be expanded to obtain p by means of Eq. 56b for the correction of the independent and the dependent coordinates. Due to the presence of E in Eq. 58, p has the required zero component wherever a coordinate has to be kept fixed and must not be changed. The corrected coordinates are required to recalculate y and X (the quantities 77 w(.s)(0) and (377gw(s)/3/i 1f ty0 for the next iteration step. In contrast to most applications of the least-squares procedure, the covariance matrix of the (effective) observations, 0- (Eq. 55) must also be recalculated because 0 depends on U which changes (though probably very little) with each step (Eq. 53). 

Using a DAE solver that accepts the Jacobian existence matrix, that is, an incidence matrix only. This provides the solver with the possibility to completely exploit the system s sparsity, but not its overall structure. Nevertheless, it is often not possible to provide the Jacobian incidence matrix, especially when the system is very large or when the incidence matrix changes as part of an iterative process. 

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