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2 x Mariolys y a
Limit and Comb
2 Marni 2
11 Limit Laws Sophie = . ..
. . b
and Limit Laws
FS: Part C
instances of discrete
25 IV.5 V.1 IX.4 presentations) Continuous Limit Laws Quasi-Powers and
Let’s denote this system by M v = y.
Gaussian limit laws Marni
Asst #3 Due
Unfortunately, such a and b do not exist, so we try to ﬁnd another vector v in
R that is a best approximation of v in the following sense: ˆ
||y − M v|| ≤ ||y − M x|| for all x ∈ R2 .
If you take the time to do the calculation, you will see that, indeed,
Dr. Marni MISHNA, Department of Mathematics, SIMON FRASER UNIVERSITY
Version of: 11-Dec-09 n (yi − (a + bxi ))2 ||y − M v|| =
i=1 so minimizing
||y − M v||
is equivalent to minimizing the least-square error, as this error is positive
and the square root is a monotone function.
Roadmap. From now, we will see how to ﬁnd such a and b (if we work in
R2 ), and more generally how to ﬁnd a best least-square approximation for a
linear system in Rn that...
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