Deduce the newton general interpolation formula
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Newton's Interpolation FormulaeNewton's Interpolation Formulae
As stated earlier, interpolation is the process of approximating a given function, whose values are known at  tabular points, by a suitable polynomial,  of degree  which takes the values  at  for  Note that if the given data has errors, it will also be reflected in the polynomial so obtained.
In the following, we shall use forward and backward differences to obtain polynomial function approximating  when the tabular points  's are equally spaced. Let

where the polynomial  is given in the following form:
 (11.4.1)
for some constants  to be determin
As stated earlier, interpolation is the process of approximating a given function, whose values are known at  tabular points, by a suitable polynomial,  of degree  which takes the values  at  for  Note that if the given data has errors, it will also be reflected in the polynomial so obtained.
In the following, we shall use forward and backward differences to obtain polynomial function approximating  when the tabular points  's are equally spaced. Let

where the polynomial  is given in the following form:
 (11.4.1)
for some constants  to be determin
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