## About the Writer

Jan M. is an amateur researcher with a keen interest in numerical methods and analysis, and the theory and applications of “special functions”. He has been playing around with computers for slightly more than two decades.

He usually does his mathematical experiments in *Mathematica*, but he is able to use other languages/computing environments to some extent.

He lives in the city of Manila, in the Philippines.

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Hey, J.M., I just now saw your 7Sep comment re Leon Hall’s Mma code for square wheels (etc.). (A flaw of MO is the lack of notification re comments.) I would like to see that code, yes. Thanks for the offer! :-j

Your blog was added to http://www.mathematica-users.org/webMathematica/wiki/wiki.jsp?pageName=Links, and your name was added to http://www.mathematica-users.org/webMathematica/wiki/wiki.jsp?pageName=User_web_pages

Feel free to modify if appropriate.

I am interested in your progress on the generalization to which you refer below:

Ack, I am in fact doing research along the lines of generalizing the Lentz-Thompson-Barnett and Steed methods to matrix arguments! The problem I’m hitting is how to properly modify the methods for the cases where certain matrices become singular. Two options come to mind: either compute the pseudoinverse, or do the equivalent of the perturbation in the scalar case and add a tiny multiple of the identity. Thus far, I’m not done with the research (too many real life things in the way). SFAIK, nobody else has looked at these generalizations before… – J. M. Jul 16 ’11 at 7:18

It may not have been noticed that the Lentz method is an LDU decomposition of the numerator and denominator matrices in the A/B matrix ratio in Abramowicz 3.10.1 and eq (3).

I would be most interested in your thoughts.

wjlentz@gmail.com

Hi,

Unfortunately, due to a number of real-life concerns, I haven’t been able to make much progress in generalizing those recursions to matrix arguments. I am aware that the three-term recurrences readily generalize to matrix arguments, but adapting the path from those recursions to the Lentz(-Thompson-Barnett) recursions has been… sticky.

So, apologies for now. Maybe someday…

Hmmm… Interesting.

I have been working on arithmetic for continued fractions including derivatives and generation methods. Please keep me in mind and let me know what can be done to motivate or cooperate with you.

wj lentz

Dear sir, thanks for the interest and apologies for the long delay in replying. I have had to put my CF-related research on hold due to real-life concerns, but I’ll surely contact you when I can resume research once more.

Wonderful site

Hello, I have seen your profile on Mathematica stack exchange, after seeing the post on modelling the solar system. I am currently working on a similar project and need some help with the mathematics. If you are willing to give me any help please let me know.

http://mathematica.stackexchange.com/questions/19268/creating-a-simulation-of-our-solar-system

Dear Sir,

your post http://mathematica.stackexchange.com/questions/275/updating-wagons-findallcrossings2d-function was extremely helpful for my research project that is to be published, and I would like to include the citation in bibliography. Could you write me your name in a private e-mail so I can credit you?

best regards

Piotr Witkowski