Backwards substitution for solving triangular linear systems.
Consider a triangular system of the form , where the vector is given, and is upper-triangular. Let us first consider the case when , and is invertible. Thus, has the form
with each , , non-zero.
The backwards substitution first solves for the last component of using the last equation:
and then proceeds with the following recursion, for :
Example: Solving a triangular system by backward substitution