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ME 581
Assignment #3
In the following questions show the derivations that you used to write your program.
1.
Write a subroutine to solve the general linear least problem normal equations:
}
{
]
[
}
]{
[
]
[
b
A
c
A
A
T
T
=
using Cholesky’s [
L
][
L
]
T
decomposition. The input to your program is matrix [
A
] and a vector {
b
}.
2.
Use the subroutine that you wrote in question #1 to find the equation of a parabola that would best fit the
equation
)
sin(
)
(
x
x
Y
=
in the interval from
x
= 0 to
x
=
π
.
Calculate an estimate of the error between the
parabola and the original function using the norm of the residual (error) vector divided by the total number
of points.
3.
In quantitative analysis in spectroscopy we are given the spectrum of 3 pure substances as:
1
i
A
,
2
i
A
and
3
i
A
where
ij
A
is the amplitude of the spectrum of substance
j
(absorbance or reflectance) at wave number
i
,
where
i
= 1 to
n
, where
n
is the total number of points in a spectrum. Suppose we have a mixture of those
substances and we measure the spectrum of the mixture
i
b
. Find the proportions of each substance in the
mixture (use the subroutine that you wrote in Question #1).
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This note was uploaded on 10/16/2011 for the course MECHANICAL 581 taught by Professor Wasfy during the Fall '11 term at IUPUI.
 Fall '11
 Wasfy
 Mechanical Engineering

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