MatLab / Progon

function [ y ] = Progon( A, F )
%UNTITLED2 Summary of this function goes here
%   Detailed explanation goes here

n = length(A) - 1;

ksi1 = A(1,2);
miu1 = -F(1);
ksi2 = A(length(A),length(A) - 1);
miu2 = -F(length(F));

for i = 2:n
   a(i-1) = A(i,i-1);
   c(i-1) = -A(i,i);
   b(i-1) = A(i,i+1);
   f(i-1) = -F(i);
end

%alpha(1) = 0;
%beta(1) = 0;
alpha(1) = ksi1;
beta(1) = miu1;

for i = 1:n-1
    alpha(i+1) = b(i)/(c(i) - alpha(i)*a(i));
    beta(i+1) = (a(i)*beta(i) + f(i))/(c(i) - alpha(i)*a(i));
end

y(n + 1,1) = (miu2 + ksi2*beta(n)) / ...
       (1 - alpha(n)*ksi2);
for i = n-1:-1:0
    y(i+1,1) = alpha(i+1)*y(i+2,1) + beta(i+1);
end
alpha
beta
end