POLYNOMIAL INTERPOLATION - LINEAR INTERPOLATION
In mathematics, linear interpolation is a method in which we instantiate a new set of data using polynomial interpolation in order to construct new data points within the range of already known points.
What does linear interpolation mean?
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In mathematics, linear interpolation is a method in which we instantiate a new set of data using polynomial interpolation in order to construct new data points within the range of already known points.
How does polynomial interpolation work?
Polynomial interpolation aims to approximate functions (tabulated or given by equations) by polynomials of degree up to n. This is intended to facilitate the calculation of functions at points that are not given (interpolating means calculating non-given internal points).
How to calculate the Interpolating Polynomial?
Since the set consists of 4 points, the interpolating polynomial must be of the form: p(x) = a₀ + a₁x + a₂x² + a₃x³, whose solution is a₀ = 1, a₁ = 6, a₂ = 0, and a₃ = -1. Therefore, the interpolating polynomial is p(x) = 1 + 6x - x³.
Polynomial Interpolation
Interpolation consists of determining a function (we will consider polynomials) that assumes known values at certain points.
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