public class BackwardSubstitution
extends java.lang.Object
Backward substitution solves a matrix equation in the form Ux = b
by an iterative process for an upper triangular matrix U.
The process is so called because for an upper triangular matrix, one first computes xn,
then substitutes that backward into the next equation to solve for xn-1,
and repeats until x1.
Note that some diagonal entries in U can be 0s, provided that the system of equations is consistent.
For example,
\[
\begin{bmatrix}
1 & 2 & 3\\
0 & 0 & 5\\
0 & 0 & 0
\end{bmatrix} \times
\begin{bmatrix}
10\\
0\\
0
\end{bmatrix} =
\begin{bmatrix}
10\\
0\\
0
\end{bmatrix}
\]
- See Also:
- Wikipedia: Forward and Back Substitution