Confluent Vandermonde with Arnoldi

In this note, we extend the Vandermonde with Arnoldi method recently advocated by Brubeck et al. (2021) to dealing confluent matrix. To apply process, it is critical find a Krylov subspace which generates column space of A theorem established for such subspaces any order derivatives. This enables us compute derivatives high degree polynomials precision. It also makes many applications involving possible, as illustrated numerical examples. We note that one approaches orthogonalizes only function values and equivalent formula given Trefethen (2022). The other approach Hermite data. About preferable another, made comparison, result problem dependent.