Before revision: This paper describes and develops a fast and accurate algorithm that computes the field of values boundary curve for every conceivable complex square matrix A, i.e., for matrices with or without repeated eigenvalues and with or without Jordan block structures  .
After revision: This paper describes and develops a fast and accurate algorithm that computes the field of values boundary curve for every conceivable complex square matrix A, i.e., for matrices with or without repeated eigenvalues and with or without Jordan block structures , with ill-conditioned eigenvalues or ill-conditioned ones and so forth .