When working with numerical code, one has to be aware of the limitations imposed by the representation of numbers in the computer and the numerical errors that algorithms invariably accumulate.

Errors

Algorithms (especially those that involve floating point numbers) generally accumulate errors. The key insight is that the total error consists of an algorithmic error (also known as the approximation error), which typically decreases with increasing the computational cost and a round-off error, which increases with the number of operations or the computational cost.

Class material

Lecture

You can follow the lecture in the notebook 08-errors.ipynb.

Example Sine Series

We will analyze the error of the sine function implementation in erroranalysis/sine-series-erroranalysis-students.ipynb. (The full solution is available as erroranalysis/sine-series-erroranalysis.ipynb.)

Additional resources for Errors

• Computational Physics: Chapter 3