Illustration of the Runge Phenomenon
Summary
Given a set of data points, interpolation by a polynomial of degree
can be bad when
is large.
Define a function
As an example, consider the smooth function .
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(1) |
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Interpolate at 5 equally-spaced points
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(2) |
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(3) |
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(4) |
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(5) |
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(6) |
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A cubic spline fit does much better
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Interpolate at a larger number of equally-spaced points
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(7) |
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A cubic spline fit does much better
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