Parlett, Beresford N.
Rights / licenseIn Copyright - Non-Commercial Use Permitted
In this paper, we analyze the distribution of the eigenvalues of glued tridiagonal matrices. Such matrices provide a useful class of test matrix because, despite being unreduced, a glued matrix can have some eigenvalues agreeing to hundreds of decimal places. A glued matrix can be obtained from a direct sum of p copies of an unreduced symmetric tridiagonal matrix T by modifying the junctions, in one of two ways, so that the new matrix has no zero off-diagonal entries. We exhibit, in gradually increasing detail, how width and placement of the eigenvalue clusters of a glued matrix depend on T, on p, and on the strength of the glue γ Show more
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Journal / seriesTechnical report / Swiss Federal Institute of Technology Zurich, Department of Computer Science
PublisherETH, Department of Computer Science
SubjectRank-1 gluing; Rank-2 gluing; EIGENVALUES OF MATRICES (ALGEBRA); Eigenvalue clusters; MATRIZEN UND LINEARE ABBILDUNGEN (ALGEBRA); Glued matrix; MATRIZENEIGENWERTE (ALGEBRA); MATRICES AND LINEAR MAPPINGS (ALGEBRA)
Organisational unit02150 - Dep. Informatik / Dep. of Computer Science
NotesTechnical Reports D-INFK.
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