# Solving large system of linear equations

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Saurabh Madankar on 16 Nov 2021
Commented: Saurabh Madankar on 16 Nov 2021
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 on 16 Nov 2021
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 on 16 Nov 2021
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.

Matt J on 16 Nov 2021
Edited: Matt J on 16 Nov 2021
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 on 16 Nov 2021
Thanks, I have got the idea now.