Approximate Solutions
The method of ordinary least squares can be used to find an approximate solution to overdetermined systems. For the system the least squares formula is obtained from the problem
the solution of which can be written with the normal equations,
where the prime sign indicates a matrix transpose, provided exists (that is, provided A has full column rank). With this formula an approximate solution is found when no exact solution exists, and it gives an exact solution when one does exist. However, to achieve good numerical accuracy, using the QR factorization of A to solve the least squares problem is preferred.
Read more about this topic: Overdetermined System
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