ME 218 Engineering Computational Methods

ME 218 Engineering Computational Methods - dc . Are they...

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ME 218 : ENGINEERING COMPUTATIONAL METHODS Home Work #3 Assigned: September 16, 2011 Due: September 22, 2011 Name: __________________UT EID: ____________Unique: _________ Lab Time: (Mon/Tue) ___PM Problem 1 (Newton Raphson Method) An engineer needs to solve the problem 0 1 ) ( 2 4 / = + = x e x f x Initial guess is at x0=1. Perform 4 iterations of the Newton Raphson’s method. Please report just 4 significant decimal digits. Problem 2 (Secant Method) Given = ! ! , solve for a root of the equation using the Secant method starting with ! = 0 ; ! = 1 . Perform 3 iterations of the Secant method and report relative error of the solution that was output by the third iteration, if you know that the actual root is at = 0 . 5671433 . Problem 3: Matrix Operations (a) Given c = 3 5 7 9 ! " # $ , and d = 0 3 6 9 ! " # $ T , compute cd and
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Unformatted text preview: dc . Are they equal? (b) Given I = 1 1 , b = 3 4 ! " # $ % & , and x = 2 1 x x , compute Ib . Is Ib equal to b ? Again, compute Ix. Is Ix equal to x ? (c) Given E 1 = 1 2 1 , E 2 = 1 3 1 , E 3 = 4 1 1 , E 4 = 1 2 1 and A = 2 3 4 2 , compute E 1 A , E 2 (E 1 A) , E 3 (E 2 E 1 A) , and E 4 (E 3 E 2 E 1 A) . Describe what is happening with rows as you multiply your matrices by E 1 , E 2 , E 3 , and E 4 , respectively. What do you notice is happening with the rows of resulting matrices (what are these matrices E 1 , E 2 ,., E 4 doing to the matrix they are multiplying from the left)?...
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