HW3 Solutions

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

This preview shows pages 1–8. Sign up to view the full content.

Problem 2.19 Vector Minimum 8 -7 4 -7 Average 11 3.4 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 )
False position method Solve f(x) = (0.8 - 0.3x) / x = 0 Input 1 5 = ε 0 Output 2.67 0 Iterations =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 19 x l = x u = x r = f(x r ) = Modified false position method Input 0.2 1.2 = ε 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....
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

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

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online