Chebyshev nodes

Chebyshev nodes are specific points used in numerical methods to approximate functions more accurately. Imagine you want to draw a smooth curve through several points; choosing these points carefully helps reduce errors and avoid issues like wild oscillations. Chebyshev nodes are spaced closer at the edges of an interval and farther apart in the middle, which minimizes the worst-case error in polynomial approximation. This strategic spacing ensures a more stable and precise interpolation or approximation, especially when dealing with complex functions, making Chebyshev nodes an essential tool for efficient and reliable numerical analysis.