Hello, I have just been given a question that I don't understand and after looking over my course notes I can't find anything resembling it. So could anyone could show me how to solve it, explain what exactly this question is about, or point me in the direction of a site that explains it clearly without too much reliance on other mathematics topics? I mainly just want to know the technique so I can do the this thing.
Any help whatsoever would be
greatly appreciated!
Let
![A=<br />
\[ \left( \begin{array}{ccccc}<br />
1 & -3 & -4 & 4 & -2\\<br />
10 & 12 & 4 & 0 & 12\\<br />
2 & 1 & 1 & 2 & 2\\<br />
-9 & -7 & 0 & -4 & -8<br />
\end{array} \right)\]<br />](http://latex.codecogs.com/png.latex?A=<br />
\[ \left( \begin{array}{ccccc}<br />
1 & -3 & -4 & 4 & -2\\<br />
10 & 12 & 4 & 0 & 12\\<br />
2 & 1 & 1 & 2 & 2\\<br />
-9 & -7 & 0 & -4 & -8<br />
\end{array} \right)\]<br />
)
Let
,
be two distinct points at which the function
)
and its first derivative
)
are defined and assume that the second derivative
)
is also defined at the point
. A Hermite interpolating quartic polynomial of the form
=\sum_{i=0}^{4} a_{i}x^{i})
can be constructed for the function
from the given five data values by determining the unknown coefficients
using the conditions:
=f(x_0))
=f'(x_0))
=f(x_1))
=f'(x_1))
and
=f''(x_1))
Construct a Hermite quartic polynomial that interpolates the function
=e^{-x})
at the eigenvalues of
by solving an appropriately defined linear system whose solution provides the coefficients
,
. Use this polynomial to construct a matrix function approximation for
.
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Hermite interpolating polynomial?
Originally Posted by zealot 
. I'll probably have to ask the lecturer about it.
