Numerical Determination of the Field of Values of a General Complex Matrix
Charles R. Johnson · SIAM Journal on Numerical Analysis · 1978
For an $n \times n$ complex matrix A, the convexity of $F(A) \equiv \{ x^ * Ax:x^ * x = 1,x \in C^n \} $ 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 $O(n^3 )$.