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Unformatted text preview: true , the true value of c, in the vector c_true. Use this to give the two
relative errors
ctrue − c 2
ˆ
ctrue − cls 2
ˆ
,
.
ctrue 2
ctrue 2
5.14 Spectrum analysis with quantized measurements. A sample is made up of n compounds, in quantities
qi ≥ 0, for i = 1, . . . , n. Each compound has a (nonnegative) spectrum, which we represent as a
vector s(i) ∈ Rm , for i = 1, . . . , n. (Precisely what s(i) means won’t matter to us.) The spectrum
+
of the sample is given by s = n qi s(i) . We can write this more compactly as s = Sq , where
i=1
S ∈ Rm×n is a matrix whose columns are s(1) , . . . , s(n) . Measurement of the spectrum of the sample gives us an interval for each spectrum value, i.e.,
l, u ∈ Rm for which
+
li ≤ si ≤ ui , i = 1, . . . , m. (We don’t directly get s.) This occurs, for example, if our measurements are quantized.
Given l and u (and S ), we cannot in general deduce q exactly. Instead, we ask you to do the
following. For each compound i, ﬁnd the range of...
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 Fall '13
 F.Borrelli
 The Aeneid

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