198 research outputs found
FPRAS for computing a lower bound for weighted matching polynomial of graphs
We give a fully polynomial randomized approximation scheme to compute a lower
bound for the matching polynomial of any weighted graph at a positive argument.
For the matching polynomial of complete bipartite graphs with bounded weights
these lower bounds are asymptotically optimal.Comment: 16 page
Equality in Wielandt's eigenvalue inequality
In this paper we give necessary and sufficient conditions for the equality
case in Wielandt's eigenvalue inequality.Comment: 6 pages, few typos are correcte
The Collatz-Wielandt quotient for pairs of nonnegative operators
In this paper we consider two versions of the Collatz-Wielandt quotient for a
pair of nonnegative operators A,B that map a given pointed generating cone in
the first space into a given pointed generating cone in the second space. If
the two spaces and two cones are identical, and B is the identity operator then
one version of this quotient is the spectral radius of A. In some applications,
as commodity pricing, power control in wireless networks and quantum
information theory, one needs to deal with the Collatz-Wielandt quotient for
two nonnegative operators. In this paper we treat the two important cases: a
pair of rectangular nonnegative matrices and a pair completely positive
operators. We give a characterization of minimal optimal solutions and
polynomially computable bounds on the Collatz-Wielandt quotient.Comment: 24 pages. To appear in Applications of Mathematics, ISSN 0862-794
Nonnegative definite hermitian matrices with increasing principal minors
A nonzero nonnegative definite hermitian m by m matrix A has increasing
principal minors if the value of each principle minor of A is not less than the
value each of its subminors. For we show has increasing principal
minors if and only if exists and its diagonal entries are less or
equal to 1.Comment: 3 page
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