# Category Archives: Numeric Analysis

## Generating Equidistant Points on Unit Disk

Recently I needed an algorithm to generate equidistant points inside the unit disk with some of them placed on the boundary (circle). To my surprise, quick search didn’t reveal any simple method for this. Below is obvious solution & code, hopefully it will save some time for others. MATLAB code: Algorithm is based on the […]

Also posted in Programming | 1 Comment

## Computing Mixed Derivatives by Finite Differences

The post is aimed to summarize various finite difference schemes for partial derivatives estimation dispersed in comments on the Central Differences page. To gather them all in one place as a reference. Listed formulas are selected as being advantageous among others of similar class – highest order of approximation, low rounding errors, etc. Please use […]

Also posted in Finite Differences, Numerical Derivative | 1 Comment

## Sinc Function and Gauss-Legendre quadrature

UPDATE: August 13, 2015. Finally I was able to see the relation between the two. Gauss-Legendre quadrature is based on exactness on polynomials, which can be re-formulated in terms of frequency domain. As it turned out, this condition has very simple form:     where $n=0,2,4,\dots,2k$ is polynomial degree and $H(\omega)$ is frequency response of […]

Also posted in Filter Design, Numerical Integration | Leave a comment