**1.22 Linear least squares**

Suppose we have a system of *M > N* equations in *N* unknowns *x _{k}*

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This problem is **over-determined** and, in general, has no solution, but it does have an approximate solution due to Carl Gauss (1777–1855).

If the matrix *A* and the vector *y* are real, then Gauss’s solution is the *N* values *x _{k}* that minimize the sum

(1.217) |

The minimizing values *x _{k}* make the

(1.218) |

or in matrix notation *A**y* = *A**Ax*. Since *A* is real, the matrix *A**A* is nonnegative ...

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