Runge's Phenomenon
A numerical analysis phenomenon discovered by German mathematician Carl Runge in 1901. It describes how high-degree polynomial interpolation of a function can produce increasingly severe oscillations near the interval endpoints as the polynomial degree grows, causing errors to rise rather than fall—demonstrating the counterintuitive principle that greater model complexity does not always yield improved accuracy.
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The Runge phenomenon refers to the fact that the higher the degree of a polynomial, the more severely the fitting error may oscillate and amplify at the two ends of the interval.
The Runge phenomenon was discovered by German mathematician Carl Runge in 1901, when he observed oscillation while performing polynomial interpolation of the function f(x)=1/(1+25x²) using equally spaced nodes.
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The Runge phenomenon refers to the fact that the higher the degree of a polynomial, the more severely the fitting error may oscillate and amplify at the two ends of the interval.
50%UnverifiedThe Runge phenomenon was discovered by German mathematician Carl Runge in 1901, when he observed oscillation while performing polynomial interpolation of the function f(x)=1/(1+25x²) using equally spaced nodes.
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