Posts

The Bregman Algorithm (2/2)
In a previous post we discussed how to find a common point in a family of convex sets by using the Bregman algorithm. Actually the algorithm is capable of more. We can use it to solve constrained optimization problems.
2021-03-13 Mathematics
Project
The Bregman Algorithm (1/2)
In the 1960s Lev Meerovich Bregman developed an optimization algorithm [1] which became rather popular beginning of 2000s. It’s not my intention to present the proofs for all the algorithmic finesse, but rather the general ideas why it is so appealing.
2021-03-06 Mathematics
Project
Optical Flow Compression Code
The matlab code for computing optimal optical flow masks for compression is avaible here. Note that the code is hardly documented and provided “as-is”. The code is released under a GPL v3 licence (unless specified differently).
2021-02-28 Programming, Software
Project
How To Create Julia Apps
A simple step by step guide to create a julia app
2020-12-27 Programming
The Abstract Interpolation Problem
We present the abstract interpolation problem and show how it is related to common interpolation and approximation tasks.
2020-10-21 Mathematics
How To Create Julia Packages
A simple step by step guide to create a julia package
2020-10-09 Programming
QR Decompositions and Rank Deficient Matrices
We discuss the necessary changes to our QR decomposition algorithms to handle matrices which do not have full rank.
2020-10-04 Mathematics
QR Comparison with other Implementations
We developed a QR decomposition algorithm, based on the orthogonalisation process of Gram-Schmidt in a series of posts here, here, here, and here. Let’s have a look how good this algorithm performs against built-in implementations from julia and other programming languages.
Last updated on 2020-12-20 Mathematics
QR Decompositions with Reorthogonalisation
Problem Formulation We already discussed QR decompositions and showed that using the modified formulation of Gram Schmidt significantly improves the accuracy of the results. However, there is still an error of about $10^3 M_\varepsilon$ (where $M_\varepsilon$ is the machine epsilon) when using the modified Gram Schmidt as base algorithm for the orthogonalisation.
2020-09-19 Mathematics
QR Decompositions
We consider the necessary changes to the Gram-Schmidt orthogonalisation to obtain a QR Decomposition
Last updated on 2020-11-15 Mathematics