Creating a Tridiagonal matrix in matlab

Question

How can I create a tridiagonal matrix that I can use for Crout factorization? And, I don't have any codes on how to create one since I am new to matlab.

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Ok, please help me understand what does the sentence "The program should output the $\infty$ norm of the residual of your computed solution and the number of iterations used" mean in this case? I am all confused figuring this out.

score 11 · Answer 1 · answered Apr 22 '14 at 01:14

>> n = 10;
>> full(gallery('tridiag',n,-1,2,-1))

ans =

     2    -1     0     0     0     0     0     0     0     0
    -1     2    -1     0     0     0     0     0     0     0
     0    -1     2    -1     0     0     0     0     0     0
     0     0    -1     2    -1     0     0     0     0     0
     0     0     0    -1     2    -1     0     0     0     0
     0     0     0     0    -1     2    -1     0     0     0
     0     0     0     0     0    -1     2    -1     0     0
     0     0     0     0     0     0    -1     2    -1     0
     0     0     0     0     0     0     0    -1     2    -1
     0     0     0     0     0     0     0     0    -1     2

Crout:

% Source: http://users.csc.tntech.edu/~mjkosa/3020/matlab/crout.m
% MATLAB implementation of Crout reduction algorithm (p. 140 of your book)
function [L,U] = crout(A,n)  % returns two matrices

for i = 1:n
    L(i,1) = A(i,1);
end

for j = 1:n
    U(1,j) = A(1,j)/L(1,1);
end

for j = 2:n
    for i = j:n
        sum = 0.0;
        for k = 1:(j-1)
            sum = sum + L(i,k) * U(k,j);
        end
        L(i,j) = A(i,j) - sum;
    end

    U(j,j) = 1;

    for i = (j+1):n
        sum = 0.0;
        for k = 1:(j-1)
            sum = sum + L(j,k) * U(k,i);
        end
        U(j,i) = (A(j,i) - sum)/L(j,j);
    end
end

Thanks. And, I can also perform Crout factorization on that and get L and U? — user136422, Apr 22 '14 at 01:16
I am getting this error while trying to execute the codes. function [L,U] = crout(A,n) | Error: Function definitions are not permitted in this context. — user136422, Apr 22 '14 at 02:05
Use $[L,U] = crout(A,n)$ then hit enter. $function [L,U] = crout(A,n)$ defines a function; which is normally done in a script not at the command line. — K. Rmth, Apr 22 '14 at 19:51

score 10 · Answer 2 · answered Nov 04 '14 at 16:13

The tridiagonal part can be created using sums of calls to diag()

n = 5 ;
nOnes = ones(n, 1) ;
x = diag(2 * nOnes, 0) - diag(nOnes(1:n-1), -1) - diag(nOnes(1:n-1), 1)

x =

     2    -1     0     0     0
    -1     2    -1     0     0
     0    -1     2    -1     0
     0     0    -1     2    -1
     0     0     0    -1     2

score 4 · Answer 3 · edited Sep 26 '16 at 19:05

4

In your case

toeplitz([2 -1 zeros(1, N-2)], [2 -1 zeros(1, N-2)])

or even

toeplitz([2 -1 zeros(1, N-2)])

edited Sep 26 '16 at 19:05

Clarissa G

103

answered Aug 06 '15 at 04:43

Yola

1,665
1
18
31

score -1 · Answer 4 · answered Nov 02 '18 at 21:17

-1

You could also use conv2 to create a tridiagonal matrix

B = conv2(eye(5),[-1 2 -1],'same');

B =

 2    -1     0     0     0
-1     2    -1     0     0
 0    -1     2    -1     0
 0     0    -1     2    -1
 0     0     0    -1     2

answered Nov 02 '18 at 21:17

Brandon Graham

1

Creating a Tridiagonal matrix in matlab

4 Answers4