Remember: You must hand in your matlab codes along with the mathematics (if needed), discussion and results.
engineering
Description
Notes:
• Remember: You must hand in your matlab codes along with the mathematics (if needed), discussion and results. Also, as indicated in class,
these codes must be commented in accordance with the examples
appearing on the website.
1. Apply Newton’s method for n > 1 dimensions to find an approximate
solution of the (“simultaneous”) pair of equations
x 3 2 /3 + x2 − x1 exp(−x 2 1 /2) = 0, x 2 1 + x 4 1 /4 = x 3 2 + 3x2. Start from (x1, x2) = (2, 2).
2. Suppose you will solve x = g(x) using a fixed-point method. Suppose
you know that |g
0
(x)| ≤ 0.3 for all x. Starting from x0 = 0, you obtain
x1 = 2.0. How many steps would be required to guarantee an error no
greater that 10−5 in your estimate of the solution? That is, if the true
solution is denoted by ¯x, what is the minimum value of n such that you
can guarantee |xn − x¯| ≤ 10−5
?
You may choose to stop based on the
number of iterations, or on a more complex condition, but your solution
approximation should be reasonably close to a true solution.
