MathTL::ExtrapolationTable< ALGORITHM, RESULT, SEQUENCE > Class Template Reference

#include <extrapolation.h>

List of all members.

Public Member Functions
	ExtrapolationTable (const ALGORITHM &T, const unsigned int size, const int p=1)
const LowerTriangularMatrix < RESULT > &	table () const
Protected Attributes
LowerTriangularMatrix< RESULT >	table_
	the extrapolation table

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Detailed Description

template<class ALGORITHM, class RESULT = double, class SEQUENCE = RombergSequence>
class MathTL::ExtrapolationTable< ALGORITHM, RESULT, SEQUENCE >

For a given generic numerical algorithm T with basic "stepsize" H and a given sequence of positive integers n_1 < n_2 < ... < n_k < ... setup the corresponding extrapolation table. The order p has to be specified (asymptotic expansion in h^p).

The algorithm T is handed over as an instance of the template parameter ALGORITHM and should provide a method

void approximate(const unsigned int n, RESULT& r) const

to compute the approximation at t+H with n "intermediate steps". For concrete problems, the interpretation of H and n can look quite differently. The Romberg quadrature, e.g., uses H as the interval length b-a, n is the number of subintervals for the trapezoidal sum. When applying extrapolation to initial value problems, H is the (time) step size and n the number of substeps.

The template parameter RESULT should be a number or vector class, since the entries of the extrapolation table are of this type.

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Constructor & Destructor Documentation

template<class ALGORITHM , class RESULT , class SEQUENCE >

MathTL::ExtrapolationTable< ALGORITHM, RESULT, SEQUENCE >::ExtrapolationTable	(	const ALGORITHM &	T,
		const unsigned int	size,
		const int	p = 1
	)

constructor with a priori fixed extrapolation table size

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Member Function Documentation

template<class ALGORITHM , class RESULT = double, class SEQUENCE = RombergSequence>

const LowerTriangularMatrix<RESULT>& MathTL::ExtrapolationTable< ALGORITHM, RESULT, SEQUENCE >::table

(

)

const [inline]

read access to the extrapolation table

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The documentation for this class was generated from the following files:

• numerics/extrapolation.h
• numerics/extrapolation.cpp