When using Newton's interpolation formula, if I get zero as a coefficient, does it mean that I have got to the most accurate description of function (such that even if I will get more points, its coefficient will be zero too)?
thank you
2026-04-01 17:10:36.1775063436
0 coefficient in newton's interpolation
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No, not by far. For example, if you have fit the points $$ (1,0), (2,0), (3,0), (4,0), (5,0) $$ with a degree-4 polynomial, that polynomial will have all zero coefficients. But if you then add the point $$ (6,120) $$ you get nonzero coefficients everywhere in the resulting degree-5 polynomial.