EE103, HW5, Winter 2009, Prof. S. E. Jacobsen
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EE103 Applied Numerical Computing, Winter 2009
Your HW answers must contain your ID, Last Name, First Name, and the number of the
Discussion Section in which you are enrolled.
The purpose of HWs is absolutely NOT for the mere assignment of grades.
purpose of HW assignments is to engage the student in the process of learning the material
of the course and the material that the instructor believes to be instructive.
As such, your
work should be your own and reflect your effort in the learning process.
As a result, you
are not to consult the notes, HWs, HW solutions, etc., of other courses or past offerings of
Of course, you may discuss the material of this course with other students of
this class; however, your work must be your own.
Prob 1 (Continuation of Prob 3 (e) of HW 4):
For the given nonlinear least squares problem under consideration, we can calculate the
Hessian and, as a result, we should be able to implement Newton’s method, rather than
G-N, and possibly solve for the optimal parameters,
You are to use the Newton code, NewtonMin.m, that has been placed at the website.
If you wish, you may modify the
The code, NewtonMin.m, requires the
use of the Hessian.
In order to use the code, you’ll need to write your function
It must take the following form:
[ ] ( )
hw p xuv
is the initial vector,
are the observations,
is the value of the
function at termination of Newton’s method, and similarly for the gradient and Hessian at
Usage of NewtonMin.m:
function xMin gx Hx
NewtonMin f x tol u v
appears in NewtonMin.m,
you’ll have to include
in the input; e.g.,
, , )
feval f xnew u v
to list your ‘hw5p1.m’, as well as your output and other comments you wish to state.
The following is a graph of the function near to what appears to be an optimal point.
By inspection, is it the case that the Hessian is PD at all points on the surface of the
If not, initiate NewtonMin.m at a point, on the graph, where the Hessian is not