Mth 351 Assignment 2 Winter 2003 Due: Mar 5, 2003
Bent Petersen 351w2003_asg02.tex
Let
f(x, y) = x2
−3y2+ 2 x y 2
−4x+ 7 y−2
g(x, y)=2x3+ 3 y2+ 6 x y −5x+ 2 y−2.
Then the nonlinear system of equations
f(x, y)=0
g(x, y)=0
can be shown to have 6 solutions,
(−2.175,−0.8586),(−1.243,1.747),(−0.4339,0.01092),
(0.4218,0.6196),(2.864,−3.173),(2.438,−4.429).
Suppose we apply Newton’s iterative method for approximating roots three times, that is, make 3 steps, starting with
the initial guess (0,0).
Problem 1. Do we appear to have convergence towards one of the roots above? Which one?
Problem 2. Compute the 2-norm of the residual vector of the last estimate found above.
You will need to do quite a bit of calculation to solve this problem and you will need to do it at fairly high precision. A
calculator, or even better, a computer is definitely needed.
Turn in a reasonable amount of work, but don’t overdo it.
Rules. You may talk to anyone and get help wherever you can for any assignment, but at some point you
must write up your work by yourself.