Numerical Methods Qualification Exam Problems and Solutions (University of Maryland)/August 2002
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Problem 1[edit | edit source]
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Solution 1[edit | edit source]
Problem 2[edit | edit source]
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[edit | edit source]
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