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Linear algebra and geometry
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Let be the Hilbert matrix of order . Starting from , execute iterations of the QR method. The element is approximately
The angular coefficient of the straight line that approximates in the least square sense the following set of points:
x=[0.2 1.14 0.54 0.87 1.25 2.36 0.19 0.54 0.51 0.33]
y=[1.25 2.36 2.58 1.87 2.68 3.41 0.65 0.47 1.36 1.25 ]
is:
Suppose you have performed the following measurements:
in ;
in ;
in ;
in .
Determine the coefficients of the order 1 exponential sum that best approximates the data in the least square sense and the norm of the corresponding residual. Those values are approximately
Suppose that the following measurements have been performed:
in ;
in ;
in .
Which are the values of the coefficients and of the regression line ?
x=[-2 -1.3 -1 -0.7 -0.4 -0.1]
y=[0.3 0.5 1.5 1.3 0.8 0.1] Which is the value of