MATH 317 Lecture Notes - Lecture 18: Band Matrix, Tridiagonal Matrix Algorithm, Lu Decomposition
15 Nov 2018
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Thmi forany a non singular in at 5 there is a decomposition. We proved it for3 3 but it"s true forany a. To solve two triangular problems using 1 substitution takes 0 operations mostuseful for solving. Symmetric positive definite matrices quite common symmetric positivedef symmetry. In the matrix can we solve with less work. First thing we don"t need piloting since let"s choose 1. Tat so we can use an as a pivot element recall that 1ststep of lu dump gave. Ail a or mil and aj aj miiajasusud. tr. _am on ii iymimi. io till i or ai li ali t. Buy ____ai an aj gi and aj. B is also symmetric and she a is symmetric aj milajwhere. mil i. Then ztbe t ztlmalme ytay70 vyiysineeaissp. di. br lblock of a which is mix n_n. The 2nd step in gaussian dim will not requirepivoting is symmetric positive rvdt to either.
