Math 2331 Linear Algebra Section 4.3 Least Squares Approximation When does Ax = b have a solution? What if there is no exact solution to Ax = b, but you need the "closest" approximation to x for an application. What do you do? The projection of b into the column space - bpe=+GJGGwhere p = And e = The projection p is the "closest" vector to the column space. Thus, e is as small as possible. So, if we find the projection of b into the column space, (i.e. find p) and then solve ±Axp=, the vector ±xis the best approximate solution to Ax = b. How do we find p? From the last section - ±TTA AxA b=
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