[thaumasiotes]

> First, you really don't want to do that division x/y, which is slow, and which fails if y==0. It's much cheaper and safer to compare "abs(x-y) < 1e-10*y".

I might be missing something, but won't your cheaper and safer fragment also fail when y is zero (or negative)?

[dmlorenzetti]

Sorry, I wasn't clear. I meant that performing the test, as originally given, will induce a divide-by-zero error. The modified test is safe against that; however, as you point out, it will still fail to indicate convergence (which is one reason to include an absolute tolerance as well).

And as you point out, you need to take the abs(y) as well, on the right-hand side.

Thanks for adding clarity.