Relevance of the additional x-x0 terms for the convergence of the additional iteration

 

1. Example: Mixing of two streams with mass and energy balance

The vector of the mass flows and enthalpies

The balance equations as auxiliary conditions

 

The functional matrix of the auxiliary conditions

 

 

The empirical covariance matrix

 

The vector of raw measurements

 

2. Iteration without the x-x0 terms

 

 

3. Iteration considering the x-x0 terms

 

4. Comparison of the variants

Both iteration schemes lead to solutions that comply with the auxiliary conditions. Without considering the terms, however, the minimum of the error sum of squares will not be reached. The solution including these terms has a lower error sum of squares. This solution is also found by a universal optimization algorithm: