lecture22 - CMPSC/MATH 451 Numerical Computations Lecture...

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Unformatted text preview: CMPSC/MATH 451 Numerical Computations Lecture 22 October 12, 2011 Prof. Kamesh Madduri Class Overview • More exercises – 5.7, 5.10 from textbook • Systems of non-linear equations – Fixed point iteration – Newton’s method 2 Nonlinear Equations Numerical Methods in One Dimension Methods for Systems of Nonlinear Equations Fixed-Point Iteration Newton’s Method Secant Updating Methods Systems of Nonlinear Equations Solving systems of nonlinear equations is much more difficult than scalar case because Wider variety of behavior is possible, so determining existence and number of solutions or good starting guess is much more complex There is no simple way, in general, to guarantee convergence to desired solution or to bracket solution to produce absolutely safe method Computational overhead increases rapidly with dimension of problem Michael T. Heath Scientific Computing 41 / 55 Nonlinear Equations Numerical Methods in One Dimension Methods for Systems of Nonlinear Equations Fixed-Point Iteration...
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lecture22 - CMPSC/MATH 451 Numerical Computations Lecture...

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