MAT 128B, Winter Programming Project 3

Programming Project 3

(due by Wednesday, March 13, 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. Submissions outside of Canvas or

after the deadline will not be accepted.

 Produce a single le for each Matlab function that you are asked to write and a single driver

le for each of the problems that you are asked to test your programs on. The driver les

should display all the quantities you are asked to print out. We will run these these driver

les to check your programs. Submit a complete set of your Matlab les as a single zip le.

When you prepare your zip le, please make sure that you zip just the Matlab les, rather

than a folder containing these les.

For this current project, you should submit a zip le of a total of 9 Matlab les: 4 les for

the functions POWER ITER, AMULT, AMULT WWW, and AMULT WWW ALPHA and

5 driver les for Problems 1{5.

 Write a short report that includes a discussion of the convergence speed of power iteration

and explanations of runs for which power iteration did not produce an approximate dominant

eigenvalue.

 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 two les: a zip le of a complete set of Matlab les

that lets us run your programs and a pdf le of your report.

The goal of this programming project is to implement and run power iteration for computing an

approximate eigenvalue and a corresponding approximate eigenvector of any matrix A 2 Rnn.

 Write a Matlab function POWER ITER that implements the version of power iteration pre-

sented in class. The inputs of this function should be a function that computes matrix-vector

products x = Au with the matrix A, an initial vector x0, a convergence tolerance TOL, and

a safeguard N0 against innite loops. The outputs should be the approximate eigenvalue 

and approximate eigenvector u produced by power iteration, the corresponding eigenvalue

residual norm

 := kAu 􀀀  uk2;

and the number j of iterations that the algorithm needed to produce the approximations 

and u.