Index

NAME

CGS - Conjugate Gradient Squared method for nonsymmetric systems

INCLUDE

include "CGS.h"

SYNTAX

 //-----------------------------------------------------------------------------
 class CGS : public KrylovItSolver
 //-----------------------------------------------------------------------------
 {

 protected:

   NUMT alpha, beta, rho, rho1;

   LinEqVector r_bar0;
   LinEqVector p;
   LinEqVector q;
   LinEqVector u;
   LinEqVector v;

   Handle(LinEqVector) y;      // Handles
   Handle(LinEqVector) t;
   Handle(LinEqVector) tmp;

   virtual bool redim (LinEqSystem& system);

 public:

   CGS ();
   CGS (const LinEqSolver_prm& pm);
  ~CGS () {}

   virtual bool ok () const;

   virtual bool solve (LinEqSystem& system);

   virtual String description () const;

   CLASS_INFO;
 };

KEYWORDS

iterative  methods,  linear systems, preconditioner, CGS, nonsym­
metric systems

DESCRIPTION

The class implements an attractive variant  of  the  Bi-Conjugate
Gradient  method, designed to solve certain classes of nonsymmet­
ric linear systems. However, CGS may lead to a  rather  irregular
convergence  behaviour  (in contrast to the Bi-Conjugate Gradient
Stabilized method, see class BiCGStab).

CONSTRUCTORS AND INITIALIZATION

There is a default constructor without arguments. For the sake of
comaptibility,  there  is  also  a constructor accepting a LinEq­
Solver_prm object, aimed to be used by LinEqSolver_prm::create.

MEMBER FUNCTIONS

ok - checks whether all the internal vectors are ready  in  addi­
tion to the standard KrylovItSolver::ok().

solve - takes an input argument of type LinEqSystem which must be
properly filled. The solution process is carried out  inside  the
function. If successful, a true value will be returned.

EXAMPLES

  Mat(real) A(4,4);
  Vec(real) x(4), b(4);
  A.scan("1 5 4 6 2 4 7 8 4 6 0 9 2 2 5 6");
  b.scan("47 63 52 45");

  LinEqSystemStd system(A,x,b);

  LinEqSolver_prm pm;
  pm.basic_method="CGS";
  pm.max_iterations=20;

  LinEqSolver* cgs = createLinEqSolver (pm);
  cgs->solve(system);

SEE ALSO

class LinEqSystem, class KrylovItSolver, class LinEqSolver_prm.

DEVELOPED BY

SINTEF Applied Mathematics, Oslo, Norway, and University of Oslo,
Dept. of Mathematics, Norway

AUTHOR

Xing Cai, UiO/SINTEF Applied Mathematics.