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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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]).