Interpolation
Interpolation is to estimate intermediate data points between other known points.
We can interpolate with various methods:
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Using a Taylor polynomial, which approximates a complex function in a given interval.
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Using a Lagrange polynomial, which generalises the behaviour of a function when all we have is a discrete set of its points.
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Newton’s finite differences interpolation method, which also helps us obtain a polynomial that generalises the behaviour of a function given a discrete set of points, but is specifically used when the differences between the abscissas are constant.
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Newton’s divided differences interpolation method, which is very similar to Newton’s finite differences method, but can work with points where the differences between the abscissas are non-constant.
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Hermite’s interpolation method, which works very similarly to Newton’s divided differences method, but uses derivatives to improve its accuracy.