Arveson studied the general problem of numerically computing spectra in this paperthis paper. The take-home message is "numerical problems involving infinite dimensional operators require a reformulation in terms of C${}^*$- algebras. Indeed, it is only when the single operator $A$ is viewed as an element of an appropriate C${}^*$-algebra $\mathcal{A}$ that one can see the precise nature of the limit of the $n \times n$ eigenvalues distributions".