Tolerance

• What is a practical tolerance for convergence?

• Cannot be less than round-off error.

• For single-precision (float) accuracy, typically take 10-6 in fractional error.

  • i.e.
  • where x = numerical solution, xr = actual root.

• When f(xr) = 0 this fails, so use  10-6 as absolute error (or perhaps use (|a| + |b|)/2).

Notes: