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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
Chebfun; Matlab
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