In this talk delivered by professor N. Trefethen it is stated that the condition number of a Vandermonde matrix of degree n verifies: $$\kappa\sim(1+\sqrt{2})^{n}$$ It is based on this paper by Gautschi. Unfortunately, I do not have access to that paper. How can I justify this approximation ?

## 1 Answer

Gautschi's paper can be downloaded from here. You may find An elementary proof of the exponential conditioning of real Vandermonde matrices more easily understandable. For real distinct nodes the condition number has the lower bound $$\kappa\geq \sqrt{\frac{2}{n+1}}\bigl(1+\sqrt 2\bigr)^{n-1}.$$