程序代写代做代考 hw4.dvi
hw4.dvi
ECS130 Homework Assignment #4 Due: 4:00pm, March 13, 2017
1. Consider the following cubic polynomial
p(x) = 816×3 − 3835×2 + 6000x− 3125.
It has three three closely spaced roots: 25/15, 25/16, 25/17
(a) Plot p(x) for 1.43 ≤ x ≤ 1.71. Show the location of the three roots.
(b) Starting with the interval [1,2], what does the bisection method do?
(b) Starting with x0 = 1.5, what does Newton’s method do?
(c) Starting with x0 = 1 and x1 = 2, what does the secant metod do?
2. Investigate the behavior of the secant method on the function
f(x) = sign(x− 2)
√
|x− 2|
Hint: start from “Example Newton 2” from our class website.
3. Let
f(x1, x2) =
1
2
(x2
1
− x2)
2 +
1
2
(1− x1)
2
(a) What is the minimizer of f(x1, x2)?
(b) Compute one iteration of Newton’s method for minimizing f(x1, x2) starting from the
point (2, 2). Is this a good step?
4. Let
f(x1, x2) =
1
2
x2
1
+
9
2
x2
2
.
It’s easy to see that the minimizer is x∗ = (0, 0)
(a) Derive the steepest descent method for finding the minimzer of of f(x).
(b) Compute the first four iterations starting from the point (9, 1).
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