MathModelingNotes2 - 4/8/2011 1 Least square and beyond...

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Unformatted text preview: 4/8/2011 1 Least square and beyond Lecture notes taken by Michael Bird on 4/7/2011 in Math Modeling I When we have data we seek to determine whether there is a relation. With these plotted points we try to fit a line to best fit all of the data ? , ? One way we can do this is to find k and m such that ? = ? + ? for = 1,2,3, , ? Writing out all of the equations for each i we see ? = ? + ? ? = ? + ? ? = ? + ? ? = ? + ? 4/8/2011 2 ? 1 = ? 1 + ? ? 2 = ? 2 + ? ? 3 = ? 3 + ? ? = ? + ? These equations can also be represented in matrix notation ? 1 ? 2 ? = 1 2 ? ? b A x given Need to find Thus our problem can be seen as = What we want is to find what our vector is so lets set our equation equal to zero = 0 Unfortunately, it is impossible to solve exactly for 0. Therefore, the plan of attack is to find k and m such that the LHS is approximately equal to the RHS or 0 How do we solve this though? One popular method is by minimizing the 2-norm 2 This particular method is known as the least square method 4/8/2011 3 ? 2 What exactly does this mean?...
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This note was uploaded on 01/16/2012 for the course MAD 4103 taught by Professor Li during the Spring '11 term at University of Central Florida.

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MathModelingNotes2 - 4/8/2011 1 Least square and beyond...

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