Chebyshev nodes are specific points used in polynomial interpolation that minimize the problem of Runge's phenomenon, particularly when approximating functions with high degrees of polynomials. These nodes are the roots of Chebyshev polynomials, which help in placing interpolation points strategically to ensure better convergence properties and reduced oscillations in the approximation. By using Chebyshev nodes, numerical methods achieve higher accuracy and efficiency in polynomial interpolation, adaptive quadrature, and other applications involving Chebyshev polynomials.
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