In the mathematical field of numerical analysis, Runge's phenomenon is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree. It was discovered by Carl David Tolmé Runge when exploring the behavior of errors when using polynomial interpolation to approximate certain functions. The discovery was important because it shows that going to higher degrees does not always improve accuracy. The phenomenon is similar to the Gibbs phenomenon in Fourier series approximations.
Read more about Runge's Phenomenon: Introduction, Problem, Related Statements From The Approximation Theory
Famous quotes containing the word phenomenon:
“If you could choose your parents,... we would rather have a mother who felt a sense of guilt—at any rate who felt responsible, and felt that if things went wrong it was probably her fault—we’d rather have that than a mother who immediately turned to an outside thing to explain everything, and said it was due to the thunderstorm last night or some quite outside phenomenon and didn’t take responsibility for anything.”
—D.W. Winnicott (20th century)