I have used linear inverse interpolation and quadratic inverse interpolation to estimate the root of a function. I found that my linear interpolation procedure required 9 iterations to achieve convergence of the root. My quadratic interpolation required just 2 iterations to converge to the root. Is it a general rule that the higher the order of the interpolatory polynomial, the quicker the convergence? If so, why?
2026-03-27 03:49:46.1774583386
Why does inverse quadratic interpolation converge quicker than inverse linear interpolation
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