#### Math

**Paper, Order, or Assignment Requirements**

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Assignment 3 for MATH 3242/CSE 3122

Winter Term 2014/2015

Due:

Solutions of Nonlinear Systems of Equations.

Read Sections 10.1 – 10.4 of “Numerical Analysis” (9th ed.) by Burden/Faires.

1. Burden/Faires p. 637, find ~x(2) for no. 7 (d) by the fixed point method (i.e. the function

iteration method) with ~x(0) = (0, 0, 0)t and show the fixed point method convergent by

checking the conditions of Theorem 10.6.

2. Burden/Faires p. 644, Use Newton’s method with ~x(0) = (0, 0, 0)τ

to compute ~x(2) for no.

2 (b).

3. Burden/Faires p. 652, Use Quasi-Newton’s method (Broyden’s method) with ~x(0) =

(0, 1)τ

to compute ~x(2) for no. 3 (b). What are the important advantages of QuasiNewton’s

method over Newton’s method?

4. Burden/Faires p. 659, Use the Steepest Decent Method with ~x(0) = (1, 0)τ

to compute

~x(1) for no. 3 (b). What is the important advantage of the Steepest Descent Method?

5. Burden/Faires p. 645, Use Newton’s method (Alg 10.1) to solve no. 6 (c). Use four

different initial guesses (two in each domain) and tolerance 10−7

. Set a table of initial

guesses, solutions, and iteration numbers. How many solutions do you find? Explain your

results.

Instructions for completing Assignment 3:

(1) Please make sure that you hand in the results with necessary intermediate steps and

explanations of your results.

(2) Question 5 should be solved by using computer. For other questions, you can solve either

manually or using computer.

(3) Besides of all results, you also need hand in a copy of your running procedures when you

use computer to solve questions.