## Quick Reference

Let *x*_{0}, *x*_{1}, *x*_{2},…, *x*_{n} be equally spaced values, so that *x*_{i}=*x*_{0}+*ih*, for *i*=1, 2,…, *n*. Suppose that the values *f*_{0}, *f*_{1}, *f*_{2},…, *f*_{n} are known, where *f*_{i}=*f*(*x*_{i}), for some function *f*. The Gregory–Newton forward difference formula is a formula involving finite differences that gives an approximation for *f*(*x*), where *x*=*x*_{0}+*θh*, and 0 < θ <1. It states thatthe series being terminated at some stage. The approximation *f*(*x*) ≈ *f*_{0}+θΔ *f*_{0} gives the result of linear interpolation. Terminating the series after one more term provides an example of quadratic interpolation.

*Subjects:*
Mathematics.

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