Lecture20 - Engineering Analysis ENG 3420 Fall 2009 Dan C....

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Engineering Analysis ENG 3420 Fall 2009 Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00
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2 Lecture 20 Lecture 20 ± Last time: ² The inverse of a matrix ² Iterative methods for solving sytems of linear equations ± Gauss-Siedel ± Jacobi ± Today ² Relaxation ² Non-linear systems ² Random variables, probability distributions, Matlab support for random variables. ± Next Time ² Linear regression ² Linear least squares regression
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Relaxation ± To enhance convergence, an iterative program can introduce relaxation where the value at a particular iteration is made up of a combination of the old value and the newly calculated value: where λ is a weighting factor that is assigned a value between 0 and 2. ² 0< λ <1: underrelaxation ² λ =1: no relaxation ² 1< λ 2: overrelaxation x i new = λ x i new + 1 − λ ( ) x i old
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Nonlinear Systems ± Nonlinear systems can also be solved using the same strategy as the Gauss-Seidel method - solve each system for one of the unknowns and update each unknown using information from the previous iteration.
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This note was uploaded on 02/17/2012 for the course EGN 3420 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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Lecture20 - Engineering Analysis ENG 3420 Fall 2009 Dan C....

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