Su96ex1 - polynomial f 3(x Use the table above and fill in...

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Su 96 EGN 3420 EXAM 1 Name________________ Problem 1 (40 pts) Consider the function f(x) = x 3 - 4x 2 + 6x - 4. Fill in the tables below and stop when the true relative error falls below 15% or after the fifth iteration, whichever comes first. Retain the maximum number of digits in all intermediate calculations; however round all displayed results in the tables to 3 places after the decimal point. Show work for one iteration to receive partial credit! A. Bisection Method Iteration # x L x U x R | e T | , % 1 0.000 10.000 2 3 4 5 B. False Position Method Iteration # x L x U x R | e T | , % 1 0.000 3.000 2 3 4 5 C. Simple One Point Iteration
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x i+1 = g(x i ) where g(x) = ______________________ i x i | e T | , % 0 1.000 1 2 3 4 5 D. Newton Raphson Method f (x) = _______________________ i x i | e T | , % 0 1.000 1 2 3 4 5 Su 96 EGN 3420 EXAM 1 Name________________
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Problem 2 (20 pts) Consider the table of values obtained from an unknown function f(x). i x i f(x i ) 2 3 0 0 0 1 1 1 2 2 2 3 4 28 a) Find the coefficients b 0 , b 1 , b 2 , and b 3 in the Newton Divided Difference Interpolating
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Unformatted text preview: polynomial f 3 (x). Use the table above and fill in the finite differences. b) Estimate the function at x=3. c) An additional data point from f(x) is x = 3, f(3) = 7. Find the true error at x=3. Su 96 EGN 3420 EXAM 1 Name________________ Problem 3 (40 pts) A) Estimate the weight of a 6 ft tall high school student using a least squares regression line thru the following data points. Height (inches) H Weight (ft) W 72 190 70 175 69 165 74 215 66 145 71 185 68 160 Hint: Use the following table to find the coefficients in the Normal Equations. H i inches W i lbs H i W i H i 2 i ˆ W 2 (W W)-e i e i 2 72 190 70 175 69 165 74 215 66 145 71 185 68 160 Σ H i Σ W i Σ H i W i Σ H i 2 2 i (W W)-∑ Σ e i 2 B) Complete the table and compute the coefficient of determination. Ans. A) ˆ (72) W = __________, B) r 2 = __________...
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This note was uploaded on 06/09/2011 for the course EGM 4320 taught by Professor Klee during the Spring '11 term at University of Central Florida.

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Su96ex1 - polynomial f 3(x Use the table above and fill in...

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