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On computing the generalized Crawford number of a matrix. (English) Zbl 1261.65044
Summary: We use methods of geometric computing combined with Hermitian matrix eigenvalue/eigenvector evaluations to find the generalized Crawford number of a pair of Hermitian matrices \(S_{1}\) and \(S_{2}\) quickly and to high precision. The classical Crawford number is defined as the minimal distance from zero in \(\mathbb C\) to the field of values of the associated complex matrix \(A=S_{1}+iS_{2}\) if zero lies outside the field of values of \(A\). We describe, test, and compare a geometry based MATLAB code for finding for the generalized Crawford number that measures the smallest distance of zero from the boundary of the field of values of \(A\) even if zero lies inside.

MSC:
65F30 Other matrix algorithms (MSC2010)
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15B57 Hermitian, skew-Hermitian, and related matrices
15A22 Matrix pencils
Software:
Chebfun; Matlab
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