Homework 5

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Homework 5

Post by Melissa on Tue Nov 01, 2011 5:36 am

I'll go ahead and get this started by saying "Lesson Learned."

Just go ahead and write a script file to do your calculations for you. Problem 7.9a takes 23 iterations, and each iteration took me half an hour to calculate by hand (I completed six). FML Mad

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Re: Homework 5

Post by Admin on Tue Nov 01, 2011 5:44 pm

For anyone needing a last minute reminder, even though the only members so far are two people other than me who have already finished the homework, the problem numbers are:

Ch 6: 1,5,19,21,24

Ch 7: 9

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Re: Homework 5

Post by Admin on Tue Nov 01, 2011 5:48 pm

Melissa wrote:each iteration took me half an hour to calculate by hand (I completed six). FML Mad

Laughing

jk. Sounds miserable.

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Re: Homework 5

Post by Melissa on Tue Nov 01, 2011 9:47 pm

6.1: I got 9 iterations with a root of 0.7686
Used the equations:
x(i+1) = sin[sqrt[x(i)]]
ea = abs[[x(i+1)-x(i)]/x(i+1)] x 100%

6.5: a) I got 6 iterations with a root of 6.4747
Used the equations:
f(x) = x^5 - 16.05x^4 + 88.75x^3 - 192.0375x^2 + 116.35x + 35.6875
f ' (x) = 5x^4 - 64.2x^3 + 266.25x^2 - 384.075x + 116.35
x(i+1) = x(i) - f[x(i)] / f ' [x(i)]
ea = abs[[x(i+1)-x(i)]/x(i+1)] x 100%
b) I got 7 iterations with a root of 5.0814
Used the equations:
f(x) = x^5 - 16.05x^4 + 88.75x^3 - 192.0375x^2 + 116.35x + 35.6875
f(x+dx) = (x+dx)^5 - 16.05(x+dx)^4 + 88.75(x+dx)^3 - 192.0375(x+dx) + 116.35(x+dx) + 35.6875
x(i+1) = x(i) - dx(i)*f[x(i)] / [f[x(i)+dx(i)]-f[x(i)]]
ea = abs[[x(i+1)-x(i)]/x(i+1)] x 100%

6.19: when w(0) = 1, w = -220.0202
when w(o) = 1000, w = 220.0202

6.21: theta = 0.6625 radians or 37.9590 degrees

6.24: numerator factors to (s+4)(s+3)(s+2)
denominator factors to (s+6)(s+5)(s+3)(s+1)
(s+3) can be eliminated from numerator and denominator

7.9: a) Took 23 iterations with a root at -0.347259424198835
Used the equations:
f(x)= x^4+2x^3+8x^2+5x
ea=(2-ϕ)|(xu-xl)/x_opt |×100%
d=(ϕ-1)(xu-xl)
x1=xl+d
x2=xu-d
b) about to work on right now Very Happy

Melissa

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Re: Homework 5

Post by Admin on Wed Nov 02, 2011 2:13 am

Melissa wrote:6.5: a) I got 6 iterations


How?? I just ran it in matlab and it runs like 22 iterations...? x(i+1) is 2.3 something at first, and then jumps way up to 90 something, and then starts shrinking down slowly. So while matlab ran all the calculations super fast, I really don't wanna write down 22 iterations lol.

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Re: Homework 5

Post by Melissa on Wed Nov 02, 2011 8:29 am

Maybe I did it wrong, because George described something like that also. If you get to class early we can compare.

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Re: Homework 5

Post by Admin on Wed Nov 02, 2011 7:24 pm

I've surrendered and aligned with George's philosophy pretty much this time around since I'm out of time. Matlab ftw! I can do the work. I just know the repetition is going to take too damn long. Done by hand, these problems really are meant to be done bout one a day--not all at once.

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