Explain why one should not use higher order polynomial interpolation. What would be a preferable method of using information from several data points for interpolation?

Higher-order polynomial interpolation, while often appealing due to its ability to pass through all data points, is generally not recommended due to several inherent issues associated with polynomial fitting. These issues arise primarily from the phenomenon of Runge's Phenomenon, which highlights the instability that occurs when high-degree polynomials are used for interpolation.

As the degree of the polynomial increases, the polynomial attempts to fit the data points perfectly, but this leads to large oscillations between points, especially when the data points are evenly ___ _______ ____ ___ ____ ________ _________ __________.
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