MAT 128B, Winter 2019
Programming Project 1
(due by Wednesday, January 30, 11:59 pm)
General Instructions
You are required to submit each of your programming projects via le upload to Canvas.
Note that the due dates set in Canvas are hard deadlines. I will not accept any submissions
outside of Canvas or after the deadline.
Write a report that includes all required numerical results, a discussion of your results, and
explanations of runs for which a method failed. Your report should be at least one page long,
but not longer than three pages.
When you are asked to print out numerical results, print numbers in 16-digit
oating-point for-
mat. You can use the Matlab command \format long e" to switch to that format from Mat-
lab's default. For example, the number 10 would be printed out as 3.141592653589793e+01
in 16-digit
oating-point format.
For each programming project, upload these les: a single pdf le of your report and a
complete set of Matlab les that lets us run and check your programs. This set should consist
of one le for each Matlab function you are asked to write and a single driver le for each
of the problems that you are asked to test your programs on. Each of these driver les
should generate the required numerical results for all runs of a problem. So for this current
project, you should submit a total of 7 Matlab les: 4 les for the functions FPI, NEWTON,
DAMPED NEWTON, and SECANT and three driver les for Problems 1{3.
We consider the problem of computing solutions of nonlinear equations
f(x) = 0; (1)
where f : R 7! R is a continuous function. A solution x of (1) is called a root of f. Newton's
method, Newton's method with damping, and the secant method are root- nding procedures that
are applied directly to the function f. Fixed-point iteration is applied to a continuous function g
the xed points of which are roots of f.
Write Matlab functions FPI, NEWTON, DAMPED NEWTON, and SECANT for carrying out the
versions of xed-point iteration, Newton's method, Newton's method with damping, and the secant
method that were presented in class. For Newton's method and Newton's method with damping,
the function f is assumed to be continuously di erentiable.
For all 4 functions, use the stopping criterion