In my numerical analysis class we have been working on approximating functions with Maclaurin Series. I am sort of confused by the definition of what makes an algorithm numerically stable. I understand that if you introduce error in the initial condition to the problem, the algorithm should still become a good approximation as the algorithm executes. My question is: When testing for stability, does the introduced error have to be very small say changing the initial condition from $1 \to .999$ or can it be large like $1 \to \frac23$?
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