Tutorial2

# Tutorial2 - Shan Feng [email protected] Determine the real...

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Shan Feng [email protected]

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Determine the real roots of f(x)=-0.5x 2 +2.5x+4.5 1) Graphically 2) Using the quadratic formula 3) Using three iterations of the bisection method to determine the highest root. Employ initial guesses of x l =5 and x u =1. Compute the estimated error and the true error after each iteration.
1) A plot indicates that roots occur at about x = –1.4 and 6.4.

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First iteration:

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Third iteration

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Determine the real root of f(x)=-26+85x-91x 2 +44x 3 -8x 4 +x 5 1) Graphically 2) Using bisection to determine the root to ε s =10%. Employ initial guesses of x l =0.5 and x u =1.0 3) Perform the same computation as in (2) but use the false-position method and ε s =0.2%
A plot indicates that a single real root occurs at about x = 0.58.

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Bisection: First iteration
The process can be repeated until the approximate error falls below 10%. As summarized below, this occurs after 4 iterations yielding a root estimate of 0.59375.

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False position: First iteration:
Second iteration:

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