منابع مشابه
Graph polynomials from principal pivoting
The recursive computation of the interlace polynomial introduced by Arratia, Bollobás and Sorkin is defined in terms of a new pivoting operation on undirected simple graphs. In this paper, we interpret the new pivoting operation on graphs in terms of standard pivoting (on matrices). Specifically, we show that, up to swapping vertex labels, Arratia et al.’s pivoting operation on a graph is equiv...
متن کاملStability of the Diagonal Pivoting Method with Partial Pivoting
LAPACK and LINPACK both solve symmetric indefinite linear systems using the diagonal pivoting method with the partial pivoting strategy of Bunch and Kaufman [Math. Comp., 31 (1977), pp. 163–179]. No proof of the stability of this method has appeared in the literature. It is tempting to argue that the diagonal pivoting method is stable for a given pivoting strategy if the growth factor is small....
متن کاملA New Principal Pivoting Scheme for Box Linear Complementarity Problems**
Judice and Pires developed in recent years principal pivoting methods for the solving of the so-called box linear complementarity problems (BLCPs) where the constraint matrices are restrictedly supposed to be of P–matrices. This paper aims at presenting a new principal pivoting scheme for BLCPs where the constraint matrices are loosely supposed to be row sufficient. This scheme can be applied t...
متن کاملTheory of Principal Partitions Revisited
The theory of principal partitions of discrete systems such as graphs, matrices, matroids, and submodular systems has been developed since 1968. In the early stage of the developments during 1968–75 the principal partition was considered as a decomposition of a discrete system into its components together with a partially ordered structure of the set of the components. It then turned out that s...
متن کاملThe Snap-Back Pivoting Method for Symmetric Banded Indefinite Matrices
The four existing stable factorization methods for symmetric indefinite pivoting (row or column exchanges) maintains a band structure in the reduced matrix and the factors, but destroys symmetry completely once an off-diagonal pivot is used. Two-by-two block pivoting maintains symmetry at all times, but quickly destroys the band structure. Gaussian reduction to tridiagonal also maintains symmet...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 1990
ISSN: 0025-5610,1436-4646
DOI: 10.1007/bf01582264