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Posts Tagged ‘ 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.

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.

25 November
Posted in Reading Diary

Solving first order PDEs with Characteristics

Use the method of characteristics to solve the PDE system

     $$\begin{cases} u_x + xu_y = 0 \\ u(0,y) = f(y) \end{cases}$$