QuestionQuestion

Transcribed TextTranscribed Text

1. (a) Write a MATLAB function x = bcksbst(U,b) that inputs a nonsingular upper triangular matrix U, and a column vector b of the same dimension and output will be a column vector x, which is the numerical solution of the linear system Ux = b obtained from the back substitution algorithm. (b) Use this function to solve the system Ux = b with 1 2 3 4 4 0 2 3 4 3 U = b = 0 0 3 4 2 0 0 0 4 1 (c) How much cpu time it takes in part (b) ? (d) Use U\b, MATLAB build-in function to solve (b), how much cpu time it takes? 2. By hand, not MATLAB, solve the following system without partial pivoting (no row interchange) - - + 6z2 + 9x3 = 39 3. Use MATLAB to generate a plot of size n of the Hilbert matrix H vs the quantity k = for n = 5.10.15 100. You will use MATLAB function hilb(n) to generate the Hilbert matrix of size n. What do you observe? Use appropriate scale for plot. (Note: k = is called the condition number of the matrix A and MATLAB has a built-in function cond(A, inf) to calculate this).

Solution PreviewSolution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

function x=bcksbst(U,b)
%Input: U Uppertriangular square matric
%       b vector
%Output: x, solutions of Ux=b

n=size(U,1);

x=zeros(size(b));

x(n)=b(n)/U(n,n);

for i=n-1:-1:1
    a=b(i);
    for j=n:-1:i+1
       a=a-U(i,j)*x(j);
    end
    x(i)=a/U(i,i);
end

return...
$30.00 for this solution

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

Find A Tutor

View available Advanced Math Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.

Decision:
Upload a file
Continue without uploading

SUBMIT YOUR HOMEWORK
We couldn't find that subject.
Please select the best match from the list below.

We'll send you an email right away. If it's not in your inbox, check your spam folder.

  • 1
  • 2
  • 3
Live Chats