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Numerical Analysis

28 October

0x5f400000: Understanding Fast Inverse Sqrt the Easy(ish) Way!

In this post, we attempt to unravel the mysteries of the “magic” constant found in the fast inverse sqrt method in an intuitive fashion.

6 November

Annoying Mclaurin Series

Suppose that we’re given the function B(z) = \frac{1 + z}{1 - z - z^2}, find the ordinary generating function associated with it in the form of B(z) = \sum_{k=0}^\infty b_k k^z. Furthermore, find/compute \sigma_n = \sum_{k=0}^n b_k.

15 October

Infinity Norm of the Inverse of Lower Bidiagonal Matrices

We consider the problem of efficiently computing the infinity norm of the inverse of a lower bidiagonal matrix L in linear time.

28 May

Introduction to Scientific Computing: Error Propagation

The first part on a series designed to survey the design and analysis of various numerical methods will look at error propagation.

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.