The stability of barycentric interpolation at the Chebyshev points of the second kind (Q466049)

The paper provides a detailed discussion of the problem of polynomial interpolation at the Chebyshev points of the second kind using the two well-known barycentric interpolation formulas from the point of view of numerical stability and rounding error propagation. The main results are: The first barycentric formula has stability problems. The root cause of these problems is discussed; it turns out that they can be overcome at the expense of severely increased run times. Assuming a specific normalization of the weights such that all weights are exactly representable in finite precision IEEE floating point arithmetic, the second barycentric formula behaves much better.