Derivation of bessel's interpolation formula for central differences
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Interpolation is the technique of estimating the value of a function for any intermediate value of the independent variable, while the process of computing the value of the function outside the given range is called extrapolation.
Central differences : The central difference operator d is defined by the relations :
Similarly, high order central differences are defined as :
Note – The central differences on the same horizontal line have the same suffix
Bessel’s Interpolation formula –
It is very useful when u = 1/2. It gives a better estimate when 1/4 < u < 3/4
Here f(0) is the origin point usually taken to be mid point, since bessel’s is used to interpolate near the centre.
h is called the interval of difference and u = ( x – f(0) ) / h, Here f(0) is term at. I hope it is useful
Central differences : The central difference operator d is defined by the relations :
Similarly, high order central differences are defined as :
Note – The central differences on the same horizontal line have the same suffix
Bessel’s Interpolation formula –
It is very useful when u = 1/2. It gives a better estimate when 1/4 < u < 3/4
Here f(0) is the origin point usually taken to be mid point, since bessel’s is used to interpolate near the centre.
h is called the interval of difference and u = ( x – f(0) ) / h, Here f(0) is term at. I hope it is useful
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