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?

In computational physics, interpolation is a crucial technique used to estimate values at points within a set of known data. However, the choice of the interpolation method can significantly impact the accuracy, stability, and efficiency of the results. Higher-order polynomial interpolation is a method that should be used with caution due to several potential drawbacks.

One of the primary reasons not to use higher-order polynomial interpolation is the phenomenon known as *Runge's phenomenon*. As the degree of the polynomial increases, the interpolated polynomial tends to oscillate between the data points, especially at the edges of the interval. This results in large errors in regions where no data ____ ____ ____ ________ ________ ___ ____ ______ __________ ________ _______ ___.
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