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Math 563 Lecture Notes Polynomial interpolation: the fundamentals

What is a short note on a polynomial interpolation?
Polynomial interpolation is the method of finding a polynomial that matches a function at specific points in its range.
More precisely, if f(x) is a function on the interval [a, b] and p(x) is a poly- nomial then p(x) interpolates the function f(x) at the points x0,x1,,xn if p(xj) = f(xj) for all j = 0, 1,,n.
How to do polynomial interpolation in Excel?
To apply polynomial interpolation in Excel, you can use the LINEST function, which is designed for linear and polynomial regressions.
The LINEST function can be used to determine the coefficients of a polynomial that fits your data.
How do you find the interpolation of a polynomial in Python?
Interpolation with python functions
The interpolant polynomial can be computed with numpy function polyfit if we choose as polynomial degree the number of the nodes minus one.
The output is the coefficients of the polynomial, from an to a0.
Global polynomial interpolation fits a smooth surface that is defined by a mathematical function (a polynomial) to the input sample points.
The global polynomial surface changes gradually and captures coarse-scale pattern in the data.

What is a short note on a polynomial interpolation?