On Gaussian elimination and determinant formulas for matrices with chordal inverses
1992 ◽
Vol 46
(3)
◽
pp. 435-440
◽
Keyword(s):
In this paper a formula is obtained for the entries of the diagonal factor in the U D L factorisation of an invertible operator matrix in the case when its inverse has a chordal graph. As a consequence, in the finite dimensional case a determinant formula is obtained in terms of some key principal minors. After a cancellation process this formula leads to a determinant formula from an earlier paper by W.W. Barrett and C.R. Johnson, deriving in this way a different and shorter proof of their result. Finally, an algorithmic method of constructing minimal vertex separators of chordal graphs is presented.
1963 ◽
Vol 59
(4)
◽
pp. 727-729
◽
2015 ◽
Vol 27
(04)
◽
pp. 1550011
◽
2017 ◽
Vol 20
(K2)
◽
pp. 107-116
2021 ◽
Vol 2090
(1)
◽
pp. 012067
Keyword(s):
Keyword(s):