Elluminate08-25-11

Elluminate08-25-11 - A E B 6 1 8 4 – P R O D U C T I O N...

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Unformatted text preview: A E B 6 1 8 4 – P R O D U C T I O N G A U S S S E I D E L E L L U M I N A T E- 2 BASIC IDEA Using a first-order Taylor series expansion ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 1 1 1 1 x x x x x x f x f x f x x x x f x f x f x x x x f x f x x x f x x = = = ∂ ≈ +- ∂ ∂- =- ∂- + = ∂ ∂ GENERAL FUNCTION • Take a general function • Suppose we want to solve for ( 29 2 exp 0.50 0.75 2 f x x x =- + + ( 29 2 exp 0.50 0.75 2 1 f x x x =- + + = GENERAL FUNCTION FIRST ORDER SETUP • Applying the first-order Taylor series expansion • To find the solution we substitute for the desired value of the function ( 29 2 exp 0.50 0.75 2 1 f x x x =- + + = ( 29 ( 29 2 1.00 0.75 exp 0.50 0.75 2 f x x x x x ∂ = - +- + + ∂ ( 29 { } ( 29 ( 29 1 1 2 1 2 1 4.4817 2 2 2.6215 5.6021 x f x f x f x x = =-- + = = + =- ∂ ∂ ITERATIONS X F(x) D f(x) 2.0000 4.4817-5.60211 2.6215 1.6989-3.17955 2.8413 1.0990-2.29846 2.8844 1.0034-2.14167 2.8860 1.0000-2.13601 TWO EQUATIONS – TWO UNKNOWNS...
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This note was uploaded on 11/08/2011 for the course AEB 6184 taught by Professor Staff during the Spring '09 term at University of Florida.

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Elluminate08-25-11 - A E B 6 1 8 4 – P R O D U C T I O N...

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