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Assignment 3 for MATH 3242/CSE 3122
Winter Term 2014/2015
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
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.