lecture18 - CMPSC/MATH 451 Numerical Computations Lecture...

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Unformatted text preview: CMPSC/MATH 451 Numerical Computations Lecture 18 October 3, 2011 Prof. Kamesh Madduri Class Overview Fixed point iteration Local convergence Newtons method 2 Nonlinear Equations Numerical Methods in One Dimension Methods for Systems of Nonlinear Equations Bisection Method Fixed-Point Iteration and Newtons Method Additional Methods Fixed-Point Problems Fixed point of given function g : R R is value x such that x = g ( x ) Many iterative methods for solving nonlinear equations use fixed-point iteration scheme of form x k +1 = g ( x k ) where fixed points for g are solutions for f ( x ) = 0 Also called functional iteration , since function g is applied repeatedly to initial starting value x For given equation f ( x ) = 0 , there may be many equivalent fixed-point problems x = g ( x ) with different choices for g Michael T. Heath Scientific Computing 18 / 55 Nonlinear Equations Numerical Methods in One Dimension Methods for Systems of Nonlinear Equations Bisection Method Fixed-Point Iteration and Newtons Method Additional Methods...
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lecture18 - CMPSC/MATH 451 Numerical Computations Lecture...

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