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 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.