Solving large system of linear equations

How to solve a large system of linear equations in MATLAB? In particular I have 31 equations and 31 unknowns and I can write these equations recursively. Say I have equations of the type c(n-1)-c(n)+c(n+1)= 0, n varying from 2 to 32 where I know the values of c(2) and c(32).

[Matt J]

Are you sure you don't mean, you know the first and the last point, c(1) and c(32)? You're trying to solve for c(2)..c(31) correct?

[Saurabh Madankar]

That is the case but I need to calculate c(0) and c(32) as well, but because of MATLAB indexing, it means I need to calculate c(1) and c(33) with c(2) and c(32) being known.

Answer 1

[Matt J]

n=32;
c(1,1)=5; c(n,1)=10; %Example data

T=toeplitz([-1,zeros(1,n-3)], [-1,1,-1, zeros(1,n-3)]);
A=T;
A(:,[1,n])=[];
b=T(:,[1,n])*[c(1);c(n)];

c(2:n-1)=A\b

c = 32×1

5 -10 -5 5 10 5 -5 -10 -5 5

[Saurabh Madankar]

Thanks, I have got the idea now.