Milan Hladík and Luc Jaulin. An eigenvalue symmetric matrix contractor. Reliab. Comput., 16:27–37, 2011.
We propose an eigenvalue contractor for symmetric matrices. Given a symmetric interval matrix $\imaceA^S$ and an interval approximation of its eigenvalue sets $\ivlłambda_1,\dots,\ivlłambda_n$ the contractor reduces the entries of $\imaceA^S$ such that no matrix with eigenvalues in $\ivlłambda_1,\dots,\ivlłambda_n$ is omitted. Our contractor is based on sequentially reducing the entries of $\imaceA^S$. We discuss properties of the method and demonstrate its performance on examples.
@article{HlaJau2011,
author ="Milan Hlad\'{\i}k and Luc Jaulin",
title = "An eigenvalue symmetric matrix contractor",
journal = "Reliab. Comput.",
fjournal = "Reliable Computing",
year = "2011",
volume = "16",
pages = "27-37",
bib2html_dl_pdf = "http://interval.louisiana.edu/reliable-computing-journal/volume-16/reliable-computing-16-pp-27-37.pdf",
bib2html_dl_html = "http://interval.louisiana.edu/reliable-computing-journal/tables-of-contents.html#Volume_16",
abstract = "We propose an eigenvalue contractor for symmetric matrices.
Given a symmetric interval matrix $\imace{A}^S$ and an interval
approximation of its eigenvalue sets
$\ivl{\lambda}_1,\dots,\ivl{\lambda}_n$ the contractor reduces
the entries of $\imace{A}^S$ such that no matrix with
eigenvalues in $\ivl{\lambda}_1,\dots,\ivl{\lambda}_n$ is
omitted. Our contractor is based on sequentially reducing the
entries of $\imace{A}^S$. We discuss properties of the method
and demonstrate its performance on examples.",
keywords = "interval matrix, interval analysis, symmetric matrix, eigenvalue",
}
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