Condition numbers of Vandermonde matrices with nearly-colliding nodes

The condition number of rectangular Vandermonde matrices with nodes on the complex unit circle is important for the stability analysis of algorithms that solve trigonometric mo- ment problems, e.g. Prony’s method. In the univariate case and with well-separated nodes, this condition number is well understood, but if nodes are nearly-colliding, the situation becomes more complicated. After recalling Prony’s method, results for the condition number of Vandermonde matrices with pairs of nearly-colliding nodes are presented. This is joint work with Stefan Kunis.