Truncation Error vs Rounding Error¶
Copyright (C) 2010-2020 Luke Olson
Copyright (C) 2020 Andreas Kloeckner
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In this notebook, we'll investigate two common sources of error: Truncation error and rounding error.
import numpy as np import matplotlib.pyplot as pt
Task: Approximate a function (here: a parabola, by a line)
center = -1 width = 6 def f(x): return - x**2 + 3*x def df(x): return -2*x + 3 grid = np.linspace(center-width/2, center+width/2, 100) fx = f(grid) pt.plot(grid, fx) pt.plot(grid, f(center) + df(center) * (grid-center)) pt.xlim([grid, grid[-1]]) pt.ylim([np.min(fx), np.max(fx)])
- What's the error we see?
- What if we make