Same code but different results

Using the same code, I get different results than those obtained on a different pc and version of Matlab (the versions involved are R2020b and R2012b). Does anyone have any idea why this is happening?

[KALYAN ACHARJYA]

Code?

[Alessandro Gottardi]

clear all
close all

n = 20000;
maxiter = 100000;
epsilon = 1.0e-10;

A = sparse(-2*eye(n)+diag(ones(n-1,1),1)+diag(ones(n-1,1),-1));

y = linspace(1,5,n)';
b = A*y;

tcpu = cputime;
[x, z, k] = coniugato(-A,-b,epsilon,maxiter);
tcpu = cputime - tcpu;

if k==maxiter
  disp('Attenzione: raggiunto il numero massimo di iterazioni');
end
if isempty(x); return; end
r = A*x-b;
fprintf('Dimensione %d, Iter %d, tcpu = %f, err = %e \n', n,k,tcpu,z(k))

and the function coniugato

function [x, z, k] = coniugato(A,b,epsilon,maxiter,x)
n = length(b);
[k,l] = size(A);
if k~=l || n~=k
    x = [];
    fprintf('Dimensioni di A e/o b non corrette \n');
    return;
end

z = zeros(maxiter,1);
if nargin<5; x=zeros(n,1); end;

r = A*x-b;
p = r;
rr = r'*r;

for k=1:maxiter;
    Ap = A*p;
    pAp = p'*Ap;
    alfa = rr/pAp;
    x = x - alfa * p;
    r = r - alfa * Ap;
    rrn = r'*r;
    z(k) = sqrt(rrn);
    if z(k)<epsilon; break; end
    beta = rrn/rr;
    p = r + beta * p;
    rr = rrn;
end

fprintf('Gradiente coniugato: ');
end

Answer 1

[Walter Roberson]

It looks to me as if you are using mrdivide ( / ) a couple of times in your code. The / operator has been improved to be able to select more efficient algorithms in some cases, and the underlying high performance math libraries have been upgraded at least twice since 2012 (my memory is saying three times for Windows, but that would have to be confirmed.)

A few years ago, the upgrades to the underlying math libraries started causing error messages in code that had run before. What had happened was that more accurate algorithms were used, but the more accurate algorithms were also more likely to detect that the problem was nearly singular — that really the old libraries should have warned about singularity too but had been a little sloppy and had permitted calculations that were not numerically meaningful.