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Extremal eigenvalue intervals of symmetric tridiagonal interval matrices
Author(s) -
Jian Yuan
Publication year - 2017
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2083
Subject(s) - tridiagonal matrix , mathematics , eigenvalues and eigenvectors , interval (graph theory) , divide and conquer eigenvalue algorithm , tridiagonal matrix algorithm , combinatorics , symmetric matrix , polynomial , discrete mathematics , mathematical analysis , physics , quantum mechanics
Summary Computing the extremal eigenvalue bounds of interval matrices is non‐deterministic polynomial‐time (NP)‐hard. We investigate bounds on real eigenvalues of real symmetric tridiagonal interval matrices and prove that for a given real symmetric tridiagonal interval matrices, we can achieve its exact range of the smallest and largest eigenvalues just by computing extremal eigenvalues of four symmetric tridiagonal matrices.