# Lecture20 - This is called successive substitution...

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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: The inverse of a matrix Iterative methods for solving sytems of linear equations Gauss-Siedel Jacobi Today Relaxation Non-linear systems Random variables, probability distributions, Matlab support for random variables. Next Time Linear regression Linear least squares regression
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. 0< λ <1: underrelaxation λ =1: no relaxation 1< λ ≤2: overrelaxation x i new x i new + 1 ( 29 x i o ld

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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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Unformatted text preview: This is called successive substitution . Newton-Raphson Nonlinear systems may also be solved using the Newton-Raphson method for multiple variables. For a two-variable system, the Taylor series approximation and resulting Newton-Raphson equations are: f 1, i + 1 = f 1, i + x 1, i + 1-x 1, i ( 29 ∂ f 1, i x 1 + x 2, i + 1-x 2, i ( 29 f 1, i x 2 x 1, i + 1 = x 1, i-f 1, i f 2, i x 2-f 2, i f 1, i x 2 f 1, i x 1 f 2, i x 2-f 1, i x 2 f 2, i x 1 f 2, i + 1 = f 2, i + x 1, i + 1-x 1, i ( 29 f 2, i x 1 + x 2, i + 1-x 2, i ( 29 f 2, i x 2 x 2, i + 1 = x 2, i-f 2, i f 1, i x 1-f 1, i f 2, i x 1 f 1, i x 1 f 2, i x 2-f 1, i x 2 f 2, i x 1 Probability and statistics concepts See class notes: Probability NASA lecture...
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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 - This is called successive substitution...

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