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ME218HW1 solutions

# ME218HW1 solutions - • This method is also relatively...

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This is the moment when we can stop because the last interval at which the function changes its sign is [0.3438 , 0.375]. This interval is narrower than 0.05 and hence we can stop here.
Problem 3 Bisection method pro/s It is rather simple and intuitive It robustly converges It only needs the sign of the function at each edge of the interval (not even the function values) For any iteration, one can analytically describe the width of the interval in which the root of the function is. Bisection method weaknesses It does not utilize very much information about the function and hence it converges very slow False position method pro/s
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Unformatted text preview: • This method is also relatively intuitive. It approximates the function with a line that passes through the function values an the edges of the interval • This method utilizes more information than the bisection method (it uses the function values rather than just the sign of the function) and hence it enables faster convergence. False position method weaknesses • One needs to calculate and utilize values of the function at the edges of the intervals (sign is not enough) • Characterizing the width of the interval in which the root of the function happens to be is now harder....
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