Numerical Determination of the Field of Values of a General Complex Matrix

For an n × n complex matrix A, the convexity of F(A) ≡ \ x^ * Ax:x^ * x = 1,x ∈ Cⁿ \ and some simple observations are exploited to determine certain boundary points and tangents of $F(A)$. The result is a convergent computation scheme and an error measure for each approximation. Given the curvature of its boundary, the computational effort to determine $F(A)$ to a prespecified level of accuracy is O(n³ ).