public class GaussianElimination extends Object
T * A == Uwhere T is the transformation matrix, U is in the row echelon form. And,
P * A == L * Uwhere P is the permutation matrix, U is lower triangular, U is in the row echelon form.
Constructor and Description |
---|
GaussianElimination(Matrix A)
Run the Gaussian elimination algorithm with partial pivoting.
|
GaussianElimination(Matrix A,
boolean usePivoting,
double epsilon)
Run the Gaussian elimination algorithm.
|
Modifier and Type | Method and Description |
---|---|
Matrix |
L()
Get the lower triangular matrix L, such that P * A = L * U.
|
PermutationMatrix |
P()
Get the permutation matrix, P, such that P * A = L * U.
|
Matrix |
T()
Get the transformation matrix, T, such that T * A = U.
|
Matrix |
U()
Get the upper triangular matrix, U, such that
T * A = U and P * A = L * U.
|
public GaussianElimination(Matrix A, boolean usePivoting, double epsilon)
A
- a matrixusePivoting
- true
if to use partial pivoting, e.g., for numerical stability.
In general, no pivoting means no row interchanges.
It can be done only if Gaussian elimination never runs into zeros on the diagonal.
Since division by zero is a fatal error we usually avoid no pivoting.epsilon
- a precision parameter: when a number |x| ≤ ε, it is considered 0public GaussianElimination(Matrix A)
A
- a matrixpublic Matrix T()
public Matrix U()
public Matrix L()
public PermutationMatrix P()
Copyright © 2010-2020 NM FinTech Ltd.. All Rights Reserved.