numerics/extrapolation.h

// -*- c++ -*-

// +--------------------------------------------------------------------+
// | This file is part of MathTL - the Mathematical Template Library    |
// |                                                                    |
// | Copyright (c) 2002-2009                                            |
// | Thorsten Raasch, Manuel Werner                                     |
// +--------------------------------------------------------------------+

#ifndef _MATHTL_EXTRAPOLATION_H
#define _MATHTL_EXTRAPOLATION_H

#include <algebra/triangular_matrix.h>

namespace MathTL
{
  class RombergSequence
  {
  public:
    unsigned int n(const unsigned int k) const { return 1<<(k-1); }
  };

  class BulirschSequence
  {
  public:
    unsigned int n(const unsigned int k) const
    {
      return (k == 1
              ? 1
              : (k%2 == 0
                 ? 1<<(k/2)
                 : 3*(1<<((k/2)-1))));
    }
  };

  class HarmonicSequence
  {
  public:
    unsigned int n(const unsigned int k) const { return k; }
  };
  
  template <class ALGORITHM, class RESULT = double, class SEQUENCE = RombergSequence>
  class ExtrapolationTable
  {
  public:
    ExtrapolationTable(const ALGORITHM& T,
                       const unsigned int size,
                       const int p = 1);

    const LowerTriangularMatrix<RESULT>& table() const { return table_; }
    
  protected:
    LowerTriangularMatrix<RESULT> table_;
  };

}

// include implementation of inline functions
#include <numerics/extrapolation.cpp>

#endif