Hello! I’m Oleksandr Kaleniuk. I do Words and Buttons Online. Just not too often lately. Last night reminded me that I probably owe my subscribers a “still alive” message. Literally still alive. So here it is. I’m still alive. As for the site, I haven’t written a new piece for about a year and, for the time being, am not planning to do so. The reason is that I’m working two jobs mid-war, and I really have no vigor left for interactive writing. The good news is that I restarted my academic career, and something good may eventually come out of it. I work at the Institute of Nuclear and Thermal Energy (https://dte.kpi.ua/pedahohichnyi-sklad/kaleniuk-oleksandr-serhiiovych/), where I teach numeric methods and explore periodic surfaces and their applications for thermal management. For instance, this is my latest work, code, examples, and whitepaper included: https://codeberg.org/okaleniuk/faitps I also built a tool for online teaching that includes all the visuals from the Words and Buttons, plus many more: https://okaleniuk.codeberg.page/blackboard/. It’s like a slide deck with interactive visuals where you get to form your deck according to your own lecture plan. I do have a lot of material to share. Some classics of numerical methods and mathematical programming, and some really hot insights, straight from the frontier of computational geometry research. So, if I manage to dodge a few more missiles and live to see the impending victory, I will definitely breathe out and come back to writing for Words and Buttons Online. But for now, I have to keep my priorities straight. Stay tuned.

An interactive demo of the Gauss-Seidel method for solving linear equation systems. When and why does it work? And why, when you flip the equations, it suddenly stop working? You can now play and see.

An interactive demo of bisection search and golden ratio search algorithms. There is also a motivation to learn them both. Spoiler alert! One converges better, and the other has a better computational cost.

An image interpolation that gives us a continuous and smooth image, where every interpolated value only depends on the four neighboring pixel values. The image becomes smooth, but sharp features remain sharp.

Rational interpolation is a step forward from polynomial interpolation towards rational splines. With rational interpolation, you can build functions that run through a set of points and also have vertical asymptotes whenever you want. With this capability, you can now model functions like logarithms better.