engr391Midterm2008

engr391Midterm2008 - Exercise 3 Fix step iteration (4...

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Department of Mechanical and Industrial Engineering ENGR 391 Numerical methods Midterm exam Read carefully all three questions Write all the steps you need to find the solution Please do not write in red (colour used for correction) Exercise 1 – General understanding (2 marks) a) Consider following polynomial: ( 29 1 2 2 + - = x x x f Why is the false position algorithm not applicable to this function? b) If you would have a computer able to computer with an infinite number of significant digits, there would be no ill-conditioned problems. True or false ? Justify or explain your answer.
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Exercise 2 – System of equations (4 marks) Consider following equations 4 0 2 9 2 2 - = - = + = + - z y y x z y x a) Write the system in Matrix form b) Decompose the A matrix in LU Show the different steps of your calculations. Hint: Check your answers at each step!
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c) Solve the system using your LU decomposition Show the different steps of your calculations. Hint: Check your answers at each step!
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Unformatted text preview: Exercise 3 Fix step iteration (4 marks) Consider following equation: (1) 1 3 2 = +-x x and following two functions: (2) ( 29 ( 29 1 3 1 2 1 + = x x g and ( 29 x x g 1 3 2-= a) Prove that (1) is equivalent to ( 29 x x g = 1 and as well equivalent to ( 29 x x g = 2 b) Plot the functions ( 29 x g 1 and ( 29 x g 2 for x between 0 and 5. x x y y c) Considering your figures from b), which one of the two functions ( 29 x g 1 and ( 29 x g 2 could you use to solve equation (1) using the fix point iteration method starting with 5 . 1 = o x ? Justify your answer by showing your iterations on your plots from figure b). d) For the function that you have chosen in c), solve equation (1) using the fix point iteration until you reach an answer with 4 significant digits ( 5 . 1 = o x ). Present your calculations in a table like : i i x ( 29 1 + i x g Error estimation 1.5 Answer:...
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engr391Midterm2008 - Exercise 3 Fix step iteration (4...

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