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Unformatted text preview: CMPSC/MATH 451 Numerical Computations Lecture 33 Nov 7, 2011 Prof. Kamesh Madduri Class Overview I gave out graded midterm exam 2 papers, and we discussed solutions to exam problems Gaussian quadrature Slides from textbook follow. 2 Numerical Integration Numerical Differentiation Richardson Extrapolation Quadrature Rules Adaptive Quadrature Other Integration Problems Gaussian Quadrature Gaussian quadrature rules are based on polynomial interpolation, but nodes as well as weights are chosen to maximize degree of resulting rule With 2 n parameters, we can attain degree of 2 n 1 Gaussian quadrature rules can be derived by method of undetermined coefficients, but resulting system of moment equations that determines nodes and weights is nonlinear Also, nodes are usually irrational, even if endpoints of interval are rational Although inconvenient for hand computation, nodes and weights are tabulated in advance and stored in subroutine for use on computer Michael T. Heath Scientific Computing 24 / 61 Numerical Integration Numerical Differentiation Richardson Extrapolation Quadrature Rules Adaptive Quadrature...
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 Spring '08
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