NewtonBase Class Reference

#include <SupportValues.h>

Inheritance diagram for NewtonBase:

Public Member Functions
	NewtonBase (const Matrix< double > &x, const Matrix< double > &y)
virtual std::string	Function () const
double	GetCoefficient (size_t index, const double &x) const
virtual Matrix< double >	Evaluate (const Matrix< double > &xIn) const
Public Member Functions inherited from PolynomialBase
	PolynomialBase (const Matrix< double > &X, const Matrix< double > &Y)
virtual Matrix< double >	Evaluate (const Matrix< double > &) const =0
virtual std::string	Function () const =0

Public Attributes
Matrix< double >	b
	newton base coefficients $$b_i$$ More...

Private Attributes
Matrix< double >	X
	support values $$x_i$$ More...

Detailed Description

Newton-Base

$$ p(x) = \sum_{i=0}^{n} b_i \omega_i(x) $$ with $$ b_i = \frac{f_{[x_{r+1}, ..., x_s]} - f_{[x_r, ..., x_{s-1}]}}{x_s - x_r} $$ and $$ \omega_i(x) = \prod_{j=0}^{i-1} (x - x_j), \quad i = 1, \dots n $$ and $$ \omega_0(x) = x_0 $$

https://wiki.godesteem.de/wiki/interpolation-and-approximation/#Newton-Base

Examples

numerics/analysis/TestSupportValues.cpp.

Constructor & Destructor Documentation

NewtonBase()

NewtonBase::NewtonBase ( const Matrix< double > &  x, const Matrix< double > &  y  )

inline

default constructor

Parameters

x	support values $$x_i$$
y	evaluated support values $$y_i$$

Member Function Documentation

Evaluate()

virtual Matrix< double > NewtonBase::Evaluate ( const Matrix< double > &  xIn ) const

inlinevirtual

Evaluate the newton base for given values

Parameters

xIn	values to evaluate

Returns

interpolated values

Implements PolynomialBase.

Function()

virtual std::string NewtonBase::Function ( ) const

inlinevirtual

String representation in newton base

Returns

representational string

Implements PolynomialBase.

GetCoefficient()

double NewtonBase::GetCoefficient ( size_t  index, const double &  x  ) const

inline

Getter for coefficient with index i for a value x

Parameters

index	index of coefficient
x	value to evaluate

Returns

evaluated coefficient

Member Data Documentation

b

Matrix<double> NewtonBase::b

newton base coefficients $$b_i$$

X

Matrix<double> NewtonBase::X

private

support values $$x_i$$

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

• include/math/numerics/analysis/SupportValues.h