Volume 28, pp. 65-77, 2007-2008.

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