cheby.h File Reference

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Functions
template<class Matrix , class Vector , class Preconditioner , class Real , class Type >
int	CHEBY (const Matrix &A, Vector &x, const Vector &b, const Preconditioner &M, int &max_iter, Real &tol, Type eigmin, Type eigmax)

Function Documentation

template<class Matrix , class Vector , class Preconditioner , class Real , class Type >

int CHEBY	(	const Matrix &	A,
		Vector &	x,
		const Vector &	b,
		const Preconditioner &	M,
		int &	max_iter,
		Real &	tol,
		Type	eigmin,
		Type	eigmax
	)

Definition at line 26 of file cheby.h.

{
  Real resid;
  Type alpha, beta, c, d;
  Vector p, q, z;

  Real normb = norm(b);
  Vector r = b - A * x;

  if (normb == 0.0)
    normb = 1;
  
  if ((resid = norm(r) / normb) <= tol) {
    tol = resid;
    max_iter = 0;
    return 0;
  }

  c = (eigmax - eigmin) / 2.0;
  d = (eigmax + eigmin) / 2.0;

  for (int i = 1; i <= max_iter; i++) {
    z = M.solve(r);                 // apply preconditioner

    if (i == 1) {
      p = z;
      alpha = 2.0 / d;
    } else {
      beta = c * alpha / 2.0;       // calculate new beta
      beta = beta * beta;
      alpha = 1.0 / (d - beta);     // calculate new alpha
      p = z + beta * p;             // update search direction
    }

    q = A * p;
    x += alpha * p;                 // update approximation vector
    r -= alpha * q;                 // compute residual

    if ((resid = norm(r) / normb) <= tol) {
      tol = resid;
      max_iter = i;
      return 0;                     // convergence
    }
  }

  tol = resid;
  return 1;                         // no convergence
}

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