## Numerical Investigation of Crouzeix’s Conjecture

Crouzeix’s conjecture states that for all polynomials p and matrices A, the inequality ||p(A)||

Crouzeix’s conjecture states that for all polynomials p and matrices A, the inequality ||p(A)||

We build upon the work of Fukuda et al.\ \cite{FuKoMuNa01} and Nakata et al.\ \cite{NaFuFuKoMu01}, in which the theory of partial positive semidefinite matrices has been applied to the semidefinite programming (SDP) problem as a technique for exploiting sparsity in the data. In contrast to their work, which improves an existing algorithm that is based … Read more