public class GaussianElimination extends Object
GaussianElimination
data type provides methods
to solve a linear system of equations Ax = b,
where A is an m-by-n matrix
and b is a length n vector.
This is a bare-bones implementation that uses Gaussian elimination
with partial pivoting.
See GaussianEliminationLite.java
for a stripped-down version that assumes the matrix A is square
and nonsingular. See GaussJordanElimination
for an alternate
implementation that uses Gauss-Jordan elimination.
For an industrial-strength numerical linear algebra library,
see JAMA.
This computes correct results if all arithmetic performed is without floating-point rounding error or arithmetic overflow. In practice, there will be floating-point rounding error; partial pivoting helps prevent accumulated floating-point rounding errors from growing out of control (though it does not provide any guarantees).
For additional documentation, see Section 9.9 Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
Constructor and Description |
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GaussianElimination(double[][] A,
double[] b)
Solves the linear system of equations Ax = b,
where A is an m-by-n matrix and b
is a length m vector.
|
Modifier and Type | Method and Description |
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boolean |
isFeasible()
Returns true if there exists a solution to the linear system of
equations Ax = b.
|
static void |
main(String[] args)
Unit tests the
GaussianElimination data type. |
double[] |
primal()
Returns a solution to the linear system of equations Ax = b.
|
public GaussianElimination(double[][] A, double[] b)
A
- the m-by-n constraint matrixb
- the length m right-hand-side vectorIllegalArgumentException
- if the dimensions disagree, i.e.,
the length of b
does not equal m
public double[] primal()
null
if no such solutionpublic boolean isFeasible()
true
if there exists a solution to the linear system
of equations Ax = b; false
otherwisepublic static void main(String[] args)
GaussianElimination
data type.args
- the command-line arguments