xerus
a general purpose tensor library
Public Member Functions | Static Public Member Functions | Public Attributes | Static Public Attributes | List of all members
xerus::misc::ShanksTransformation< ft_type > Class Template Reference

Limit extraction using the shanks transformation aka Aitken process. More...

#include <simpleNumerics.h>

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Public Member Functions

virtual ~ShanksTransformation ()
 
ft_type best_estimate () const override
 
ft_type error_approximate () const override
 
void push_back (ft_type _val) override
 
void reset () override
 
- Public Member Functions inherited from xerus::misc::LimitExtractor< ft_type >
virtual ~LimitExtractor ()
 

Static Public Member Functions

static ft_type shanks (ft_type x1, ft_type x2, ft_type x3)
 

Public Attributes

std::vector< ft_type > values
 

Static Public Attributes

static constexpr ft_type epsilon = std::numeric_limits<ft_type>::epsilon()
 

Detailed Description

template<class ft_type>
class xerus::misc::ShanksTransformation< ft_type >

Limit extraction using the shanks transformation aka Aitken process.

Can be derived by assuming the sequence to go as \( x_n = x_inf + alpha * q^n \) for large \( n \).

Definition at line 106 of file simpleNumerics.h.

Constructor & Destructor Documentation

◆ ~ShanksTransformation()

template<class ft_type >
virtual xerus::misc::ShanksTransformation< ft_type >::~ShanksTransformation ( )
inlinevirtual

Definition at line 122 of file simpleNumerics.h.

Member Function Documentation

◆ best_estimate()

template<class ft_type >
ft_type xerus::misc::ShanksTransformation< ft_type >::best_estimate ( ) const
overridevirtual

Implements xerus::misc::LimitExtractor< ft_type >.

Definition at line 275 of file simpleNumerics.cpp.

◆ error_approximate()

template<class ft_type >
ft_type xerus::misc::ShanksTransformation< ft_type >::error_approximate ( ) const
overridevirtual

Implements xerus::misc::LimitExtractor< ft_type >.

Definition at line 284 of file simpleNumerics.cpp.

◆ push_back()

template<class ft_type >
void xerus::misc::ShanksTransformation< ft_type >::push_back ( ft_type  _val)
overridevirtual

Implements xerus::misc::LimitExtractor< ft_type >.

Definition at line 267 of file simpleNumerics.cpp.

◆ reset()

template<class ft_type >
void xerus::misc::ShanksTransformation< ft_type >::reset ( )
overridevirtual

Implements xerus::misc::LimitExtractor< ft_type >.

Definition at line 293 of file simpleNumerics.cpp.

◆ shanks()

template<class ft_type >
ft_type xerus::misc::ShanksTransformation< ft_type >::shanks ( ft_type  x1,
ft_type  x2,
ft_type  x3 
)
static

Definition at line 258 of file simpleNumerics.cpp.

Member Data Documentation

◆ epsilon

template<class ft_type >
constexpr ft_type xerus::misc::ShanksTransformation< ft_type >::epsilon = std::numeric_limits<ft_type>::epsilon()
static

Definition at line 108 of file simpleNumerics.h.

◆ values

template<class ft_type >
std::vector<ft_type> xerus::misc::ShanksTransformation< ft_type >::values

Definition at line 110 of file simpleNumerics.h.

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