Show that the elements of the LR decomposition $ T=L R $ can be expressed by tridiagonal matrices $ T $ with
can be determined by the following recursive relation:
How could you prove this statement clearly (I don't really have any ideas)? Then I should calculate the LR decomposition of the matrix $ T $ in the case $ n=12, b_{i}:=c_{i+1}:=-2 $ for $ i=1, \ldots, 11 $, $ a_{i}:=4 $ for $ i=1, \ldots, 12 $ - how do I do that for this general example?