solve_tridiag.m

function x=solve_tridiag(ud,uo,lo,b);
%solve_tridiag The purpose of this function is to solve common equation
%Ax=b given the diagonal of the upper matrix(ud), and the off diagonals
%(uo,lo) and the vector b. The procedure similar to Cholesky factorization.

n = length(b); %set dimension of n based on input vector
x = zeros(n,1); %create an empty vector to store values of length n
y = zeros(n,1); % create an empty vector to store values of length n that will be manipulated
y(1) = b(1); %Assign the first y value to equal the first value of vector b (equal to one)

%Set up iterative procedure to back solve for the vectors of the off
%diagonals. (similar to Cholesky's step procedure).
for i=2:n %for loop beginning with second element 
    y(i)=b(i)-lo(i-1)*y(i-1); %utilize the first given input to calculate the first value of the lower off diagonal
    
end

x(n) = y(n)/ud(n); 
for i=n-1:1 %procedure to algebraically find the values  of the upper diagonal
    x(i)=(y(i)-uo(i)*x(i+1))/ud(i);
end