# Questions tagged [catastrophic-cancellation]

For questions about catastrophic cancellation, the devastating loss of precision when small numbers are computed from large numbers, which themselves are subject to roundoff error.

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### How do I fight loss of significance and/or improve convergence for this recursive algorithm?

While trying to answer this question I used the series approach and obtained a recursive algorithm. While checking it numerically, I found it suffering from "catastrophic cancellation", i.e. loss of ...
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### Avoiding numerical cancellation question for $\sin x -\sin y$ for $x \approx y$

When trying to avoid cancellation, one tries to reformulate the equation in order to avoid subtraction between almost equal terms. In $\sin (x) - \sin (y), x \approx y$ the suggested solution is to ...
Define the following four rational numbers.  a = \frac{4243257079864535154162785598448178442416}{41016602865234375} \\ b = -\frac{143308384621912247542172258992236503771301}{1210966757832031250} \\ ...