Using MATLAB, setup and run the error minimization approach to solving the system of equations , writing out the estimate at each iteration along with the error.

2/3 x + y + 1/2 z = 3

1/2 x + 2/3 y + z = 2

x + 1/2 y + 2/3 z = 1

In this case we will compute the iteration matrix and the vector value once at the beginning of the program and then use them repeatedly in the iteration loop. The program should use a of 0.3 and preform about 100 iterations. The solution should be similar to the solution found in part 1, however the program does not need to compare the two solutions.

Prototype:

// Open file for recording output

// Then compute

Iter = // ( I - mu * A' * A )

bIter = // and mu * A' * b

x = // random data.

for k = 0:100

// Perform iteration.

y = Iter * x + bIter;

// Compute error vector

e = A*x b;

e = e' * e; // The sum squared error

// Replace x with y.

x = y;

// Write x, and error to the previously opened file.

// Exit if sqrt( e )

end

i+1