Interface BiconjugateGradient

public interface BiconjugateGradient

The biconjugate gradient method to solve systems of linear equations.

Field Summary

Fields

Modifier and Type	Field	Description
static final org.slf4j.Logger	logger

Method Summary

Static Methods

Modifier and Type	Method	Description
static double	solve(Matrix A, Vector b, Vector x)	Solves A * x = b by iterative biconjugate gradient method with Jacobi preconditioner matrix.
static double	solve(Matrix A, Vector b, Vector x, Preconditioner P, double tol, int itol, int maxIter)	Solves A * x = b by iterative biconjugate gradient method.

Field Details

logger

static final org.slf4j.Logger logger

Method Details

solve

static double solve(Matrix A,
 Vector b,
 Vector x)

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

Parameters:

A - the linear system.

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 set to the improved solution.

Returns:

the estimated error.

solve

static double solve(Matrix A,
 Vector b,
 Vector x,
 Preconditioner P,
 double tol,
 int itol,
 int maxIter)

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

Parameters:

A - the linear system.

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 set to the improved solution.

P - 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.