1,938 reputation
1519
bio website go.helms-net.de
location Germany
age 61
visits member for 4 years, 4 months
seen 20 hours ago
Mathematics is only a hobby - although I have done undergrad courses in the 70ties. But part of my job was doing statistics and this kept me near my favourite subject "linear algebra" (programmed factor-analysis and a matrix-orientated calculator MatMate). Around 2002 I came in contact with the internet-community in math-newsgroups and could improve my Collatz-discussion. Next subject was the Bernoulli-numbers, then integer matrices and since 2006 the problem of iterated exponentiation aka tetration. Serving half-term jobs in teaching here at the university I found time to fiddle with that subjects in depth - and found love with the exploratory approach and impulse of the 18'th century numbertheory, namely L.Euler, "the master of us all"... Due to lack of formal education I've to do my "research" widely on my own - but that's what I just like: to find structure, pattern, laws from the ground.

Nov
20
revised formal power series convergence
improved formatting
Nov
15
comment Is rigour just a ritual that most mathematicians wish to get rid of if they could?
I too come late to this thread and for me fedja's essay is fully comprehendable and I agree even with that topics which vote for critical reflection of what and how mathematicians are doing. I think the tone of "sour-ness" does not revert the meaningfulness of the said, but might be a result of being eremite with that thoughts.
Nov
10
awarded  Organizer
Nov
10
revised iterative solution better than analytic solution?
added tag for numerical algorithms
Nov
10
revised iterative solution better than analytic solution?
added 136 characters in body
Nov
10
suggested suggested edit on iterative solution better than analytic solution?
Nov
10
answered iterative solution better than analytic solution?
Oct
21
comment How did the summation operation come into use?
Hmm, isn't that question (and that answer as well) more appropriate designed for wikipedia?
Oct
6
comment The difference between Principal Components Analysis (PCA) and Factor Analysis (FA)
(...) After we've chosen the FA-model, and decided to respect the itemspecific variance: then we have the option to define (from theory or some earlier study) the amount of that part of variance -as large as possible, or possibly even zero or also slightly correlated. In fact (and is little known) the programmed estimation of the itemspecific error (based on the inversion of the covariance matrix) does not give the maximal possible sum of item-specific error-variance; by manually experimenting with this (when I've studied the method again) I could arrive at higher sums.
Oct
6
comment The difference between Principal Components Analysis (PCA) and Factor Analysis (FA)
The focus of the first sentence (1) and that of the enhanced-formatted one (2) are diametral. In fact it is the statistical model which gives the basis for the correct choice. In (2) it is correctly added that the covariance matrix admits both models. But then proceeds with a "rank"-argument (a purely mathematical one) instead of the statistical argument. (...)
Oct
4
revised Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity
edited body
Oct
4
revised Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity
edited body
Oct
4
revised Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity
added 650 characters in body
Oct
4
revised Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity
added 650 characters in body
Oct
4
comment Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity
@ChristianRemling : When I asked this I was relatively new to the method of Jordan decomposition and the question "how to explain" should have better been asked as "how to understand". After much reading and exercising I think I've understood this now.
Oct
4
revised Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity
added 1051 characters in body
Oct
4
revised Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity
added 1051 characters in body
Oct
4
accepted Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity
Oct
4
revised Trouble with Jordan form of the truncated Carleman-matrix for $\sin(x)$ as size $n$ goes to infinity
added 722 characters in body
Oct
1
comment Summation mollifier to ensure a certain alternating series has the correct value
Very well; I use Euler-summation with configurable order. The order must be adapted: when the series to mollify is $1-1+1-1...$ order 1 is needed, when it is $1-3+9-27+81-...+...$ order 3 is needed and so on. If I see it correctly the current proposal is the matrix (or a matrix very near to that) for Euler-summation of order 1. But after your last formula it seems that you can circumvent quotients of absolute values $ \gt 1$, so that matrix should sufffice for all cases and no additional consideration is needed.