com.numericalmethod.suanshu.matrix.doubles.linearsystem

Class ForwardSubstitution

java.lang.Object

com.numericalmethod.suanshu.matrix.doubles.linearsystem.ForwardSubstitution

public class ForwardSubstitution
extends java.lang.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 x_n. Note that some diagonal entries in L can be 0s, provided that the system of equations is consistent. For example, \[ \begin{bmatrix} 0 & 0 & 0\\ 2 & 0 & 0\\ 4 & 5 & 6 \end{bmatrix} \times \begin{bmatrix} 0\\ 0\\ 30 \end{bmatrix} = \begin{bmatrix} 0\\ 0\\ 30 \end{bmatrix} \]

See Also:

Wikipedia: Forward substitution

Constructor Summary

Constructors

Constructor and Description
ForwardSubstitution()

Method Summary

Modifier and Type	Method and Description
Vector	solve(LowerTriangularMatrix L, Vector b) Solve Lx = b.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ForwardSubstitution

public ForwardSubstitution()

Method Detail

solve

public Vector solve(LowerTriangularMatrix L,
                    Vector b)

Solve Lx = b.

Parameters:

L - a lower triangular matrix, representing the system of linear equations (the homogeneous part)

b - a vector

Returns:

a solution x such that Lx = b

Throws:

LinearSystemSolver.NoSolution - if there is no solution to the system