Nested matrices and inverse $M$-matrices

Stuart, Jeffrey L.. "Nested matrices and inverse $M$-matrices." Czechoslovak Mathematical Journal 65.2 (2015): 537-544. <http://eudml.org/doc/270111>.

@article{Stuart2015,
abstract = {Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the $LU$- and $QR$-factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse $M$-matrices with symmetric, irreducible, tridiagonal inverses.},
author = {Stuart, Jeffrey L.},
journal = {Czechoslovak Mathematical Journal},
keywords = {nested matrix; tridiagonal matrix; inverse $M$-matrix; principal minor; determinant; $QR$-factorization},
language = {eng},
number = {2},
pages = {537-544},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nested matrices and inverse $M$-matrices},
url = {http://eudml.org/doc/270111},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Stuart, Jeffrey L.
TI - Nested matrices and inverse $M$-matrices
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 537
EP - 544
AB - Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the $LU$- and $QR$-factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse $M$-matrices with symmetric, irreducible, tridiagonal inverses.
LA - eng
KW - nested matrix; tridiagonal matrix; inverse $M$-matrix; principal minor; determinant; $QR$-factorization
UR - http://eudml.org/doc/270111
ER -