Discuss the methods of inerpolation for unequally spaced ordinates c++
Answers
Explanation:
Newton's divided difference interpolation formula is a interpolation technique used when the interval difference is not same for all sequence of values.
✍✍✍✍ Suppose f(x0), f(x1), f(x2 f(xn) be the (n+1) values of the function y=f(x) corresponding to the arguments x=x0, x1, x2…xn, where interval differences are not same.
Answer:
Explanation:
Here, (a1−ao),(a2−a1) etc. are not equal. The problem of interpolation requires that X=Xo , and the value of f(Xo) must be found. In order to determine the value of f(Xo) we need to compute the divided difference.
The quantities
f(a1)−f(ao)a1−ao denoted by f(a1,ao)
f(a2)−f(a1)a2−a1 denoted by f(a2,a1)
f(a3)−f(a2)a3−a2 denoted by f(a3,a2)
etc.
are called divided difference of the first order. Moreover, the quantities
f(a2,a1)−f(a1,ao)a2−ao denoted by f(a2,a1,ao)
f(a3,a2)−f(a2,a1)a3−a1 denoted by f(a3,a2,a1)
etc.
are called the divided differences of the second order. Similarly, the divided difference of order three and higher may be computed.