Answer: In mathematics, the method of polynomial interpolation is a method for constructing a polynomial function that passes through a given set of points. The polynomial function constructed in this way is called an interpolating polynomial. It is used to approximate a function when it is known only at a few discrete points, and the goal is to find a smooth curve that fits the data as closely as possible.
The method of polynomial interpolation involves finding the polynomial of the lowest degree that passes through a given set of points. This is done by setting up a system of equations using the coordinates of the points, and then solving for the coefficients of the polynomial. Once the coefficients are known, the polynomial function can be evaluated at any point within the domain of the data points.
There are several different techniques that can be used to find the interpolating polynomial, such as the Lagrange interpolation, Newton's divided differences method and the least-squares method. The choice of method will depend on the specific problem and the desired properties of the interpolating polynomial.
In summary, the method of polynomial interpolation is a technique used to construct a polynomial function that passes through a given set of points. It is used to approximate a function when it is known only at a few discrete points and aims to find a smooth curve that fits the data as closely as possible.
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