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//*****************************************************************
// Iterative template routine -- CHEBY
//
// CHEBY solves the symmetric positive definite linear
// system Ax = b using the Preconditioned Chebyshev Method
//
// CHEBY follows the algorithm described on p. 30 of the
// SIAM Templates book.
//
// The return value indicates convergence within max_iter (input)
// iterations (0), or no convergence within max_iter iterations (1).
//
// Upon successful return, output arguments have the following values:
//
// x -- approximate solution to Ax = b
// max_iter -- the number of iterations performed before the
// tolerance was reached
// tol -- the residual after the final iteration
//
//*****************************************************************
//
// Slightly modified version of IML++ template. See ReadMe file.
//
// Jesper Andersson
//
#ifndef cheby_h
#define cheby_h
namespace MISCMATHS {
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)
{
Real resid;
Type alpha, beta, c, d;
Vector p, q, z;
Real normb = b.NormFrobenius();
Vector r = b - A * x;
if (normb == 0.0)
normb = 1;
if ((resid = r.NormFrobenius() / 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 = r.NormFrobenius() / normb) <= tol) {
tol = resid;
max_iter = i;
return 0; // convergence
}
}
tol = resid;
return 1; // no convergence
}
} // End namespace MISCMATHS
#endif // End #ifndef cheby_h