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.


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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