Calculator Demonstration of Numerical Stability

The proliferation of hand-held calculators gives new relevance and urgency to the plea of the late G.E. Forsythe that users of numerical methods be made aware of the pitfalls of floating point computation. Although roundoff errors may remain negligible, they usually propagate to some extent, and in extreme cases, if the algorithm is unstable (very sensitive to perturbations caused by roundoff), the calculated values may be totally false. Calculator users should therefore be aware of the limitations of their instruments.