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 onto x_n.

Note that some diagonal entries in L can be 0s, provided that the system of equations is consistent. E.g.,

 | 0 0 0 |     |  0 |   |  0 |
 | 2 0 0 | %*% |  0 | = |  0 |
 | 4 5 6 |     | 30 |   | 30 |
 

See Also:

Wikipedia: Forward substitution

Field Summary

LowerTriangularMatrix

L the system of linear equations (the homogeneous part)

Constructor Summary

ForwardSubstitution(LowerTriangularMatrix L)
Construct a ForwardSubstitution instance to solve for different Vector b's.

Method Summary

Vector

solve(Vector b) Solve Lx = b

Methods inherited from class java.lang.Object

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

Field Detail

L

public final LowerTriangularMatrix L

the system of linear equations (the homogeneous part)

Constructor Detail

ForwardSubstitution

public ForwardSubstitution(LowerTriangularMatrix L)

Construct a ForwardSubstitution instance to solve for different Vector b's.

Parameters:

L - a lower triangular matrix

Method Detail

solve

public Vector solve(Vector b)

Solve

Lx = b

Parameters:

b - a vector

Returns:

x such that

Lx = b

Throws:

Solver.NoSolution - if there is no solution to this system