Further Examples: Interpolation

Approximating Sqrt

Here is a table of values of the square root function at the points .

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This constructs an approximate function that represents these 10 values on the domain .

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The values of the function match the data at the given points.

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The function sqrt1 also gives a fair approximation to the square root function at other points between and .

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A plot of the difference between the two functions shows that the approximation is better at some points than at others.

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Here is another set of data that gives values of the square root function as well as its derivatives at the points .

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Here is the corresponding interpolating function.

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The values of this function likewise match the data at the given points.

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Here is the plot of the difference between the square root function and sqrt2.

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This shows that in general sqrt2 gives a significantly better approximation to the square root function than sqrt1 does.

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Finding Closest Integers

This defines the function closestIntegers which returns the integers in list1 that are closest to those in list2.

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Periodic Interpolation

This creates an InterpolatingFunction object which repeats itself periodically. The data at the endpoints of the fundamental period must match: otherwise the function would not be periodic.

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In more than one dimension, you can specify that some dimensions be repeated periodically and that others are not by giving the value of the option as a list. This sets up an InterpolatingFunction which will be periodic in the second dimension but not in the first.

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