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Solving an overdetermined linear system

Let , where has m components and has n components.

Suppose we have k>n measurements , and wish to recover .

Form matrices and by adjoining and , respectively. NOTE: is not square.

The matrix can be recovered as follows. Define an error vector with m components:

Adjoining the k error vectors, we get

The sum of the squares of the errors is

Differentiate and equate to 0:

The term is the pseudoinverse of .

Edelman Shimon
Tue Nov 7 09:13:01 EET 1995