How (Un)stable Are Vandermonde Systems?

Many problems in applied and numerical analysis eventually boil down to solving large systems of linear algebraic equations. Since the matrices and right-hand sides of such systems are typically the result of (sometimes extensive) computations, they are subject to an unavoidable level of noise caused by the rounding errors committed during their generation. It is then a matter of practical concern trying to estimate the effect of such uncertainties upon the solution of the system. A common answer and one which we shall adopt in the sequel concerning any nonsingular system