Runge's Phenomenon

Runge's Phenomenon describes a mathematical issue where interpolating a smooth function with high-degree polynomial curves using equally spaced points leads to large oscillations near the edges of the interval. As the degree of the polynomial increases, instead of accurately approximating the original function, the curve can wildly oscillate and diverge from the true values, especially at the interval's boundaries. This counterintuitive behavior highlights limitations of polynomial interpolation, demonstrating that more complex models aren't always better for capturing a function’s behavior, and that careful choice of points or alternative methods are often necessary.