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 backwards substitution
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