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MATH 3795 Lecture 14 Polynomial Interpolation

What is the formula for interpolation of polynomials?
Typical problems in this class include polynomial interpolation Φ(x;a0,,an) = a0 + a1x + a2x2 + ··· + anxn, as well as trigonometric interpolation Φ(x;a0,,an) = a0 + a1exi + a2e2xi + ··· + anenxi (i2 = −1).
How do you interpolate 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.
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.
Matlab Built-in Polynomial Interpolation: polyfit
The basic function-call is p=polyfit(x,y,m), where x is a vector of �� independent values, y is the corresponding vector of �� dependent values and �� = �� − 1.
The function returns the coefficient vector of the (�� − 1)-order interpolation polynomial.

What is the formula for interpolation of polynomials?