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The structured distance to normality of an irreducible real tridiagonal matrix. (English) Zbl 1171.65037

Summary: The problem of computing the distance in the Frobenius norm of a given real irreducible tridiagonal matrix \(T\) to the algebraic variety of real normal irreducible tridiagonal matrices is solved. Simple formulas for computing the distance and a normal tridiagonal matrix at this distance are presented. The special case of tridiagonal Toeplitz matrices also is considered.

MSC:

65F30 Other matrix algorithms (MSC2010)
65F50 Computational methods for sparse matrices
15B57 Hermitian, skew-Hermitian, and related matrices
65F35 Numerical computation of matrix norms, conditioning, scaling
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