I'm used to provide the context before asking the real question. However, I noticed that this writing style leads to very poor automatically generated previews on the main page:
Notation for Gauss-Newton method Non-linear least squares problems are often solved by the Levenberg-Marquardt algorithm, which can be viewed as a Gauss–Newton method using a trust region approach. ...
Another issue with my style is that the real question ends up somewhere in the middle of the question text, because further clarifications and additional related questions naturally occur at the end of the question text. Additionally, I was recently notified in a comment that my way to provide context can be distracting.
I'm thinking about how to rewrite the two affected questions, and how to adapt my writing style in general to better match the expectations of this site. I guess it would be sufficient if I would start with the real question, clarify what is actually unclear to me, and then continue in my usual writing style to provide the context and further related questions.
Further clarification and related questions
This question itself is actually a typical example of my writing style. The real question ended up somewhere in the middle of the question text, because I added further clarifications and related questions at the end of the question text. One reason why I'm sometimes tempted to add related questions at the end is that I fear that my real question is too difficult (Convergence of Gauss-Newton) or too broad to generate any answers that will help me on my further research. An example of a too broad question (that I actually didn't post) is "How to model non-existence (or not-yet existence) mathematically?" I came up with this question as an answer to the closed question New branches of math?. This question is too broad, but the theory of stochastic processes and the Bayesian probability current have developed some partial answers to it, and some of my questions related to these solution approaches are actually quite specific and could probably be answered (even if I'm not sure if these questions would be appropriate for this site).