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Could you tell me where can I read about method of full reduction (it is method for system of linear equations with triangular matrix).

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Where did you hear about this? What context? – J. M. Dec 9 '10 at 1:00
I heard that from one professor before. This method is a bit old. At the moment people do not study that in university because it's work only for small variety of cases (work for some triangular matrix), but this method has complexity of O(n). So, that's work really fast. – Andriy Dec 9 '10 at 22:49
Andriy: The "cyclic reduction" I am familiar with works on (block) tridiagonal matrices. It would be nice if you could mention the Russian book where you encountered this method. – J. M. Dec 23 '10 at 3:13
Could this be what you are looking for?… – Federico Poloni Dec 23 '10 at 8:28

I have never heard of the "method of full reduction" (neither has Google), but a standard textbook on matrix computation is... "Matrix computation", by Golub and van Loan. For sparse matrix stuff (almost almost irrelevant for your question) a great book is Tim Davis' little book called "direct methods for the solution of [something or other]).

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Thanks for the information! This method is old and it could be only in old book, which was written 40 years ago (around 40). The other name for this method is "method of cyclic reduction". I am not sure about translation (I do direct translation from Russian and in Russian it is like "метод полной редукции", "метод циклической редукции" or "метод Тратенберга"). I also tried to find it with google but... I did not find anything. – Andriy Dec 9 '10 at 23:18

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