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6 handout 1 self study singularity analysis which 2can

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Unformatted text preview: . 2 x Mariolys y a 18 IX.1 Limit and Comb Laws 2 Marni 2 11 Limit Laws Sophie = . .. Random Structures 20 IX.2 Discrete . . . . b . . and Limit Laws FS: Part C Combinatorial 23 IX.3 Mariolys yn 1 xn (rotating instances of discrete 12 25 IV.5 V.1 IX.4 presentations) Continuous Limit Laws Quasi-Powers and Let’s denote this system by M v = y. 13 30 IX.5 Gaussian limit laws Marni Sophie 14 Dec 10 Presentations Asst #3 Due ˆ Unfortunately, such a and b do not exist, so we try to find another vector v in 2 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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