# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.algebra.linear.matrix.doubles.linearsystem

## Class ForwardSubstitution

• java.lang.Object
• com.numericalmethod.suanshu.algebra.linear.matrix.doubles.linearsystem.ForwardSubstitution

• public class ForwardSubstitution
extends Object
Forward substitution solves a matrix equation in the form Lx = b by an iterative process for a lower triangular matrix L. The process is so called because for a lower triangular matrix, one first computes x1, then substitutes that forward into the next equation to solve for x2, and repeats until xn. Note that some diagonal entries in L can be 0s, provided that the system of equations is consistent. For example, $\begin{bmatrix} 0 & 0 & 0\\ 2 & 0 & 0\\ 4 & 5 & 6 \end{bmatrix} \times \begin{bmatrix} 0\\ 0\\ 30 \end{bmatrix} = \begin{bmatrix} 0\\ 0\\ 30 \end{bmatrix}$