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January, 2013

18 January

Fixing floating point cancellation I

How can you compute \sqrt{x^2+1}-x to 14 digits of accuracy within the domain |x| < 10^8?

17 January
Posted in Numerical Analysis

Floating point quirks

In this post, we’ll explore a scenario where the non-commutativityassociativity of floating point arithmetic can lead us into trouble.

Let a_k = \frac{1}{k(k+1)} and S_n = \sum_{k=1}^n a_k. Write a computer program to compute this sum.