lecture17 - CMPSC/MATH 451 Numerical Computations Lecture...

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CMPSC/MATH 451 Numerical Computations Lecture 17 September 30, 2011 Prof. Kamesh Madduri
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This class Convergence rate Intermediate value theorem Interval bisection Slides from textbook follow 2
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Nonlinear Equations Numerical Methods in One Dimension Methods for Systems of Nonlinear Equations Nonlinear Equations Solutions and Sensitivity Convergence Convergence Rate For general iterative methods, define error at iteration k by e k = x k - x * where x k is approximate solution and x * is true solution For methods that maintain interval known to contain solution, rather than specific approximate value for solution, take error to be length of interval containing solution Sequence converges with rate r if lim k →∞ k e k +1 k k e k k r = C for some finite nonzero constant C Michael T. Heath Scientific Computing 13 / 55
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Nonlinear Equations Numerical Methods in One Dimension Methods for Systems of Nonlinear Equations Nonlinear Equations Solutions and Sensitivity Convergence Convergence Rate, continued
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lecture17 - CMPSC/MATH 451 Numerical Computations Lecture...

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