## 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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