This is in continuation of: Stability Regions for Varah's Formulas Design Notes on System for the Analysis of Order- and Stepsize Changes for Cyclic Composite Multistep Methods Tendler-like Formulas for Stiff ODEs Below is the output of: rm -f /tmp/v3c stabregion4 -f Varah7 -o3 -r100 -L4:-9:22:15 | grep -Fv...

1. Consistency 2. Parasitic roots 3. Stability region 4. Comparison James Varah created six linear multistep methods with zero roots at infinity, i.e., $A_\infty^0[\alpha]$-stable methods. These methods share this property with the BDF. For the terminology see Tendler-like Formulas for Stiff ODEs. This post gives...

1. Stability region 2. Stability mountain 3. Cryer's k-step methods Colin Cryer in his article on $A_0$-stable methods mentioned in passing that there is a method, which is $A_0$-stable but not $A[\alpha]$-stable for any $\alpha$. For the terminology see Tendler-like Formulas for Stiff ODEs. This post shows the...

This blog uses Pagefind to provide search on this website. I had written on this here: Pagefind: Searching in Static Sites. In a first step I already removed the ca. 118 kB large pagefind-ui.js. Now I have gone full lazy-loading. I have added this to my CSS. The highlighted lines are changed to what Grok in a...

This is a continuation of the post Performance Comparison: gzip vs Brotli three years ago. Here we will present measurements for three compression algorithms (gzip, brotli, and zstd) employed on two different hardware architectures (AMD and ARM). The measurements cover all possible compression levels. Input data are...

1. Google Search is the most prominent search engine. There have been multiple and repeating complaints about Google Search getting worse. For example, The End of Google Search—and the Internet—as We Know It Google isn’t the best search engine anymore Google Search May Be Deindexing URLs At Higher Rates We have to...

I explored the possibility of employing Content Security Policy for this very blog. I succeeded in enforcing a couple of URL whitelists. But that showed that whenever the referring websites change anything on their end, I am cooked. Below is an NGINX configuration to allow for JavaScript libraries like MathJax...

This post shows how to call the GUPTRI algorithm from C. The GUPTRI algorithm solves the generalized eigenvalue problem $A x = \lambda B x$. The algorithm can properly handle the cases when $A$, $B$, or both matrices are singular. Bibliography. Demmel, James and Kagstrom, Bo: “The Generalized Schur Decomposition of...

Here we analyze the two methods from Eldon Hansen (1969). These are two cyclic linear multistep methods of order $p=5$ and $p=7$. The first one only needs 3 starting values for order 5. The second one only need 4 starting values and reaches order 7. Both methods break the first Dahlquist barrier. They can do that...

Brittney Lowe Hartley discusses why she is an atheist. TLDR: Men created God for their specific purposes. God didn't create men. The TikTok video was converted to text using tokscript. Then Google Gemini added headings, emphasis, punctuation by asking: Add punctuation to below text: ... The TikTok video in question...

Here we analyze the three methods from Christoph Fredebeul, which were mentioned in Albrecht (1989). These are three cyclic linear multistep methods of order $p=3$ and $p=4$. They should not to be confused with the A-BDF from Fredebeul. Bibliography. Peter Albrecht: “Elements of a General Theory of Composite...

1. Problem statement There are some bots which request lots of pages of my web-server, which do not exist. This post shows how these bots are blocked on the network level with iptables. Here is an example of excessive HTTP 404 errors: 34.165.43.146|04/Jun/2026:12:43:33 +0200|404|14589|GET /backup.zip...