08 Errors

02 Mar 2021

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 for Errors

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

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

Additional resources for Errors

• Computational Physics: Chapter 3