Question

Why polynomial interpolation preferred over trigonometric functions?

Answer 1

hiiii mate here your answer ✔️ ✔️
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In case of interpolation, the function ϕ(x)ϕ(x) to approximate the unknown function f(x)f(x) may be polynomial, exponential, trigonometric sum, Taylor's series, piece-wise polynomial etc. Then why polynomial interpolation is considered as better than others (although I know that there is a justification for approximation by polynomials (Weierstrass's theorem), but it does not true that there is no justification to approximate by exponential, trigonometric etc).

Some where I read, reason for considering the polynomials in the approximation of functions f(x)f(x) is that the derivative and indefinite integral of a polynomial are easy to determine and are also polynomials. But if ϕ(x)ϕ(x) is exponential, trigonometric sum, Taylor's series, piece-wise polynomial etc then also derivative and indefinite integral are determined like polynomials.

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❤️ I hope you mark as brainlist answer⭐❤️✨✨✨✨

Answer 2

plzz mark this above answer mark as brainlist answer ✨✨