Transcription of EE364a Homework 3 solutions
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EE364a Homework 3 solutions
EE364a , Winter 2007-08 Prof. S. BoydEE364a Homework 3 , .. , fn:R Rbe given continuous functions. Weconsider the problem of approximatingf0as a linear combination off1, .. , fn. Forx Rn, we say thatf=x1f1+ +xnfnapproximatesf0with tolerance >0 overthe interval [0, T] if|f(t) f0(t)| for 0 t T. Now we choose a fixed tolerance >0 and define theapproximation widthas the largestTsuch thatfapproximatesf0over the interval [0, T]:W(x) = sup{T||x1f1(t) + +xnfn(t) f0(t)| for 0 t T}.Show thatWis show thatWis quasiconcave we show that the sets{x|W(x) }areconvex for all.
EE364a Homework 3 solutions 3.42 Approximation width. Let f0,...,fn: R → R be given continuous functions. We ... Use part (c) to verify that f ... 4.8 Some simple LPs. Give an explicit solution of each of the following LPs. (a) Minimizing a linear function over an affine set. minimize cTx subject to Ax = b.
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