EGN3420F97Final - the Gaussian-elimination algorithm. I...

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EGN 3420 Final Fall 1997 4:00 - 6:50 PM Open notes, open book and can use calculator. Write on test sheets. Use the back of the sheet if necessary. Show all work for partial credit and explain how you are going to solve the problem. NAME______________________________ SS#________________________________ 1. (12.5%) Find the positive root of f(x). Use 2 iterations of the bracket method first to find an initial approximation then use Newton's method to further improve your estimate to 4 digits of accuracy. f x ( ) x 2 17.384 x . 60.387628 The plot f x ( ) x 0 5 10 15 50 0 50 100
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2. (12.5) Find a 2 nd order polynomial to approximate f(x) = sin(x) around x = PI/2. Find an upper bound for the error. Hint: use the Taylor series. 3. (12.5%) What is the error of f(x,y,z) if x = 10, y = 5 and z = 3 where x has an error of 1 and y has an error of 3. f x y , z , ( ) x 2 y . y z . x z . 5
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4. (12.5%) Find using the Hamilton-Cayley theorem. Find an expression in terms of A. A 3 for A 1 2 0 4
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5. (12.5%) Solve the following linear system using Gaussian-elimination. You must use
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Unformatted text preview: the Gaussian-elimination algorithm. I know that you know how to solve it. I want to see if you know the Gaussian-elimination algorithm. x 3 3 3 x 1 . 4 x 2 . x 3 8 2 x 1 . x 2 x 3 2 6. (12.5%) Find the 3 nd order polynomial that best fits the data. Find the set of simultaneous equations that must be solved. Do not solve them just mention what steps you would take from that point to find the coefficients of the polynomial. x f(x) 0 -1 1 1 2 1 3 0 4 -1 7. (12.5%) Given the following 4 points find a 3 nd order Lagrange interpolating polynomial that passes through the points. You do not need to simplify the polynomial. x f(x) -1 3 0 3 1 7 2 21 8. (12.5%) Given the following function in tabular form, integrate the function from 1 to 7. Use the multiple application version of Simpson's 1/3. There should be only 1 equation. x f(x) 1 2 2 4 3 5 4 4 5 3 6 4 7 5...
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EGN3420F97Final - the Gaussian-elimination algorithm. I...

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