In many examples of numerical instability (e.g., overflow, underflow, catastrophic cancellation, etc), we encounter issues with maintaining high precision.
One way to "know" what the "right" answer is would be to leverage fixed precision methods to validate our answers. One such Python package that gives us fixed precision is mpmath.
We can/should consider using it where necessary.
Here is one example where catastrophic cancellation (subtraction of two numbers) raises a problem that can be verified by fixed precision math.
In many examples of numerical instability (e.g., overflow, underflow, catastrophic cancellation, etc), we encounter issues with maintaining high precision.
One way to "know" what the "right" answer is would be to leverage fixed precision methods to validate our answers. One such Python package that gives us fixed precision is mpmath.
We can/should consider using it where necessary.
Here is one example where catastrophic cancellation (subtraction of two numbers) raises a problem that can be verified by fixed precision math.