lecture13_final - CMPSC/MATH 451 Numerical Computations...

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Unformatted text preview: CMPSC/MATH 451 Numerical Computations Lecture 13 September 21, 2011 Prof. Kamesh Madduri Review of last class Modified problems Sherman-Morrison formula Improving accuracy Diagonal scaling Iterative refinement Cholesky factorization Factoring banded systems 2 This class Software for solving linear systems of equations (and general linear algebra problems) netlib.org we looked at web sites for BLAS and LAPACK Top500 list uses GE with partial pivoting as the benchmark for ranking supercomputers We started discussing solutions to systems of non-linear equations See corresponding slides from textbook. 3 Nonlinear Equations Numerical Methods in One Dimension Methods for Systems of Nonlinear Equations Nonlinear Equations Solutions and Sensitivity Convergence Nonlinear Equations Given function f , we seek value x for which f ( x ) = 0 Solution x is root of equation, or zero of function f So problem is known as root finding or zero finding Michael T. Heath Scientific Computing 3 / 55 Nonlinear Equations...
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This note was uploaded on 01/19/2012 for the course CMPSC 451 taught by Professor Staff during the Spring '08 term at Pennsylvania State University, University Park.

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lecture13_final - CMPSC/MATH 451 Numerical Computations...

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