Divergence (Runge phenomenon) for least-squares polynomial approximation on an equispaced grid and mock-Chebyshev subset interpolation
Consider the approximation of a given function analytic in \((-1,1)\) by a \(N\)th degree polynomial that is chosen to minimize the least squares error at \(P\) equidistant points in the interval \([-1,1]\). Numerical evidence is presented that indicates that the Runge phenomenon which is present in the case \(P = N+1\) can be weakened, but not completely eliminated, for \(P \gg N+1\).
scientific article; zbMATH DE number 5550285