13. Interpolation Method - Deepstash

13. Interpolation Method

He was the first who propose an interpolation formula using second-order difference. His Sanskrit verses on this formula were found in the Khandakadyaka work of Brahmagupta. Today, the Brahmagupta interpolation formula is known as Newton- Stirling interpolation formula. In his book, he termed the difference Dr as the ‘gatakhanda’, the difference Dr+1 as the ‘bhogyakhanda’, ‘Vikala’ as the quantity in minutes by which the interval has been covered at the point of interpolation, which in modern notation denoted as a− xr. ‘Sphuta-bhogyakhanda’ is now known as fr+1 − fr.

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