Numerical Methods Qualification Exam Problems and Solutions (University of Maryland)/August 2002
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Problem 1
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Solution 1
[edit | edit source]Problem 2
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Suppose there is a quadrature formula
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Solution 2
[edit | edit source]All nodes lies in (a,b)
[edit | edit source]Let be the nodes that lie in the interval .
Let which is a polynomial of degree .
Let which is a polynomial of degree .
Then
since is of one sign in the interval since for ,
This implies is of degree since otherwise
from the orthogonality of .
All weights positive
[edit | edit source]Problem 3
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