[SOLVED] matlabECS130 Homework Assignment #1

ECS130 Homework Assignment #1 Due: 4:00pm, January 23, 2017

1. (a) Derive, mathematically, the back substitution method for solving the upper trian-

   gular linear system

   Ux = b
   using componentwise, row-oriented and column-oriented algorithms, respectively.

   (b) Write three MATLAB functions:

   x = mybscomponent(U,b)x = mybsrow(U,b)x = mybscolumn(U,b)

   for the componentwise, row-oriented and column-oriented algorithms, respectively.

   (c) Test the correctness of your functions and compare the execution time of these functions for a set of different sizes of upper triangular linear systems.

2. Modify the lutx function to a new function called mylutx so that it uses explicit for loops instead of MATLAB vector notation. For example, one section of your modified program will read

    % compute the multipliers for i = k+1:n

    A(i,k) = A(i,k)/A(k,k); end

   Test the correctness of your function mylutx, and compare the execution time of mylutx with lutx and with the built-in lu function by finding the order of the matrix for which each of the three programs takes about 10 seconds on your computer.

3. The inverse of an n n matrix A can be defined as the matrix X whose columns xj solve the equations

   Axj = ej for j = 1,2,,n, where ej is the jth column of of the identity matrix.

   (a) Starting with the function bslashtx, write a MATLAB function X = myinv(A) that computes the inverse of A. Your function should call lutx only once and should not use the built-in MATLAB backslash operator or inv function.

   (b) Test your function by comparing the inverses it computes with the inverses ob- tained from the built-in inv(A) on a few test matrices, say from gallery collection in MATLAB.

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