## The structured distance to normality of an irreducible real tridiagonal matrix

S. Noschese, L. Pasquini, and L. Reichel

### Abstract

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.

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### Key words

matrix nearness problem, distance to normality, real tridiagonal matrix, eigenvalue conditioning, Toeplitz matrix

### AMS subject classifications

65F30, 65F50, 15A57, 65F35

### ETNA articles which cite this article

 Vol. 36 (2009-2010), pp. 99-112 Laura Smithies: The structured distance to nearly normal matrices

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