Defeating the Runge phenomenon for equispaced polynomial interpolation via Tikhonov regularization

AbstractRunge showed that polynomial interpolation using an equispaced grid often diverges as the degree N of the interpolating polynomial fX increases, even when f(x) is analytic over the whole interval. We suppress Runge divergence by defining the approximating polynomial as the minimizer of the sum of the interpolation residual plus a constant - times a smoothness norm. The Tikhonov parameter - can be determined easily through the method of the L-shaped curve. The resulting “Tikhonov approximant” is at least as accurate as the truncated, Nth degree Chebyshev series for the same function