Gregory Newton Backward Formula
Gregory-Newton Backward Interpolation Formula is similar to the forward formula but is used when data points are given in reverse order. The formula is given by:
f(x) = yn + (x – xn)Δyn /h + (x – xn)(x – xn-1)Δ2yn /2!h2 + (x – xn)(x – xn-1)(x – xn-2)Δ3y0 /3!h3 +…
where,
Differences Δyn, Δ2yn, … are Calculated Backward and
- h is Common Difference Between x-values
- f(x) is Interpolated Function Value at Point x
- xn, xn-1, xn-2,… is Given Data Points (in Descending Order)
- Δyn, Δ2 yn… is Backward Differences
- Δyn = yn-1 – yn
- Δ2yn = yn-2 – yn-1
Gregory Newton Interpolation Formula
Newton-Gregory Forward Interpolation Formula is an interpolation method when our data points are evenly spaced. Interpolation is a method in maths used to make educated guesses about values between two points we already know. We can say that the Gregory–Newton forward difference formula involves finite differences that give an approximate value for f(x), where x = x0 + θ.h, and 0 < θ <1. Approximation of f(x) ≈ f0 + θ.Δf0 gives the result of Linear Interpolation.
Here in this article learn about, the Newton-Gregory Interpolation Formula, its Examples, and others in detail.
Table of Content
- What is Gregory Newton’s Formula?
- Gregory Newton Forward Formula
- Gregory Newton Backward Formula
- Applications Of Gregory Newton Formula
- Examples on Gregory Newton Difference Formula
- Practice Questions on Gregory Newton’s Formula
- Gregory Newton Formula FAQs