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.

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.

Answer 1

>> 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

Answer 2

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

Answer 3

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)])