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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 1994 • Question 4

Question

Math 6610 • Analysis of Numerical Methods I Fall 1994 • Question 4

a) What set of four nonlinear equations are satisfied by the nodes and weights for Gaussian quadrature with degree of precision 3, on the interval \([0,1]\).

b) Describe Newton’s method as applied to solving this system of equations.

c) Show how and why the weights and nodes for Gaussian quadrature may be modified from the standard interval to an arbitrary interval.

Raw LaTeX

\textbf{a)} What set of four nonlinear equations are satisfied by the nodes and
weights for Gaussian quadrature with degree of precision 3, on the interval
\([0,1]\).

\textbf{b)} Describe Newton's method as applied to solving this system of
equations.

\textbf{c)} Show how and why the weights and nodes for Gaussian quadrature may be
modified from the standard interval to an arbitrary interval.

Topic Tags

Gaussian Elimination and Pivoting Linear Programming and Optimization Numerical Quadrature Quadrature Rules