smile.math.matrix

Class BiconjugateGradient

java.lang.Object

smile.math.matrix.BiconjugateGradient

public class BiconjugateGradient
extends java.lang.Object

The biconjugate gradient method is an algorithm to solve systems of linear equations.

Constructor Summary

Constructors

Constructor and Description
BiconjugateGradient()

Method Summary

Modifier and Type	Method and Description
static Preconditioner	Jacobi(DMatrix A) Returns a simple preconditioner matrix that is the trivial diagonal part of A in some cases.
static double	solve(DMatrix A, double[] b, double[] x) Solves A * x = b by iterative biconjugate gradient method with Jacobi preconditioner matrix.
static double	solve(DMatrix A, double[] b, double[] x, Preconditioner preconditioner, double tol, int itol, int maxIter) Solves A * x = b by iterative biconjugate gradient method.

Methods inherited from class java.lang.Object

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

Constructor Detail

BiconjugateGradient

public BiconjugateGradient()

Method Detail

Jacobi

public static Preconditioner Jacobi(DMatrix A)

Returns a simple preconditioner matrix that is the trivial diagonal part of A in some cases.

solve

public static double solve(DMatrix A,
                           double[] b,
                           double[] x)

Solves A * x = b by iterative biconjugate gradient method with Jacobi preconditioner matrix.

Parameters:

b - the right hand side of linear equations.

x - on input, x should be set to an initial guess of the solution (or all zeros). On output, x is reset to the improved solution.

Returns:

the estimated error.

solve

public static double solve(DMatrix A,
                           double[] b,
                           double[] x,
                           Preconditioner preconditioner,
                           double tol,
                           int itol,
                           int maxIter)

Solves A * x = b by iterative biconjugate gradient method.

Parameters:

b - the right hand side of linear equations.

x - on input, x should be set to an initial guess of the solution (or all zeros). On output, x is reset to the improved solution.

preconditioner - The preconditioner matrix.

tol - The desired convergence tolerance.

itol - Which convergence test is applied. If itol = 1, iteration stops when |Ax - b| / |b| is less than the parameter tolerance. If itol = 2, the stop criterion is that |A^-1 (Ax - b)| / |A^-1b| is less than tolerance. If tol = 3, |x_k+1 - x_k|₂ is less than tolerance. The setting of tol = 4 is same as tol = 3 except that the L_∞ norm instead of L₂.

maxIter - The maximum number of iterations.

Returns:

the estimated error.