HW3 Solutions - 19 x l = x u = x r = f(x r ) = Modified...

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Problem 2.19 Vector Minimum 8 -7 4 -7 Average 11 3.4 1
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Problem 2.20 Input matrix -5 1 2 7 3 0 4 -1 6 -3 1 0 Normalized matrix -0.71 0.14 0.29 1 0.75 0 1 -0.25 1 -0.5 0.17 0
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Problem 5.5 0.1 2 n = 20 x y 0.1 0.1 0.2 0.19 0.3 0.27 0.4 0.33 0.5 0.35 0.6 0.35 0.7 0.3 0.8 0.21 0.9 0.05 1 -0.16 1.1 -0.44 1.2 -0.8 1.3 -1.23 1.4 -1.76 From the plot, we note that the first nontrivial root is approximately equal to 0 1.5 -2.38 1.6 -3.1 1.7 -3.92 Estimate the number of iterations for the bisection method: 1.8 -4.86 1.9 -5.91 2 -7.09 n = 4.644 = 5 iterations x min = x max = (x u - x l ) / 2 n = 0.02 2 n = 25 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
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Bisection method Input 0.5 1 = ε 0.02 Ouput 0.91 0.94 Check: 0.92 0.01 0.9. x l = x u = x l = x u = x r y(x r )
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False position method Solve f(x) = (0.8 - 0.3x) / x = 0 Input 1 5 = ε 0 Output 2.67 0 Iterations =
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Unformatted text preview: 19 x l = x u = x r = f(x r ) = Modified false position method Input 0.2 1.2 = Output - MFPM 1 Iterations = 10 Output - FPM 1 Iterations = 21 The performance of the modified false position method is better. It converges to the root more than twice as fast as the standard false position method. Remember that error estimates in the false position method can be misleading! Solve f(x) = x 10- 1 = 0 x l = x u = x r = f(x r ) = x r = f(x r ) = Also, the actual function value at x r is closer to 0 with the modified false position method....
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HW3 Solutions - 19 x l = x u = x r = f(x r ) = Modified...

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