Systems of linear equations and their general solutions

2 Systems of linear equations and their general solutions 

Let us consider again a system of linear equations determining the relationship between the observed data di, 2,, and parameters of the model mi, m2, m3. 

However we have more data di,d2,d3,. ..,d/v than model parameters mi, m2, m3,. .., m/,, so we cannot fit all the data. The best that we can do is to minimize 

Functional / is called a misfit functional. It can be written in the form 

Note that, using matrix notations, one can rewrite the last equation in the form 

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