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Unformatted text preview: s criterion
N ( f ( t k ) − yk ) 2 . k=1 We will use B-splines to parametrize f , so the variables in the problem are the coeﬃcients x in
f (t) = xT g (t). The problem can then be written as
subject to x T g ( t k ) − yk k=1
x T g ( t) 2 (21) is convex in t on [α0 , αM ]. (a) Express problem (21) as a convex optimization problem of the form
Ax − b
subject to Gx h. 2
2 (b) Use CVX to solve a speciﬁc instance of the optimization problem in part (a). As in the ﬁgures
above, we take M = 10 and α0 = 0, α1 = 1, . . . , α10 = 10.
Download the Matlab ﬁles spline_data.m and bsplines.m. The ﬁrst m-ﬁle is used to generate
the problem data. The command [t, y] = spline_data will generate two vectors t, y of
length N = 51, with the data points tk , yk .
The second function can be used to compute the B-splines, and their ﬁrst and second derivatives, at any given point u ∈ [0, 10]. The command [g, gp, gpp] = bsplines(u) returns
three vectors of length 13 w...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
- Fall '13
- The Aeneid