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971.
C. He 《Numerische Mathematik》1997,76(4):463-477
Summary. According to the methodology of [6], many measures of distance arising in problems in numerical linear algebra and control
can be bounded by a factor times the reciprocal of an appropriate condition number, where the distance is thought of as the
distance between a given problem to the nearest ill-posed problem. In this paper, four major problems in numerical linear
algebra and control are further considered: the computation of system Hessenberg form, the solution of the algebraic Riccati
equation, the pole assignment problem and the matrix exponential. The distances considered here are the distance to uncontrollability
and the distance to instability.
Received November 4, 1995 / Revised version received March 4, 1996 相似文献
972.
David M. Mason 《Journal of multivariate analysis》1984,14(2):181-200
One and two sample rank statistics are shown in general to be more efficient in the Bahadur sense than their sequential rank statistic analogues as defined by Mason (1981, Ann. Statist.9 424–436) and Lombard (1981, South African Statist. J.15 129–152), even though the two families of statistics (those based on full ranks and those based on sequential ranks) have the same Pitman efficiency against local alternatives. In the process, general results on large deviation probabilities and laws of large numbers for statistics based on sequential ranks are obtained. 相似文献
973.
We investigate the following problem: What countable graphs must a graph of uncountable chromatic number contain? We define two graphsΓ andΔ which are very similar and we show thatΓ is contained in every graph of uncountable chromatic number, whileΔ is (consistently) not. 相似文献
974.
J. Širáň 《Periodica Mathematica Hungarica》1984,15(4):301-305
We prove that the crossing number of graphs with connectivity 2 has in certain cases an additive property analogous to that
of crossing number of graphs with connectivity ≤1. 相似文献
975.
Eric David Belsley 《Probability Theory and Related Fields》1998,112(4):493-533
When run on any non-bipartite q-distance regular graph from a family containing graphs of arbitrarily large diameter d, we show that d steps are necessary and sufficient to drive simple random walk to the uniform distribution in total variation distance, and
that a sharp cutoff phenomenon occurs. For most examples, we determine the set on which the variation distance is achieved,
and the precise rate at which it decays.
The upper bound argument uses spectral methods – combining the usual Cauchy-Schwarz bound on variation distance with a bound
on the tail probability of a first-hitting time, derived from its generating function.
Received: 2 April 1997 / Revised version: 10 May 1998 相似文献
976.
Recently, linear programming problems with special structures have assumed growing importance in mathematical programming.
It is well known that exploiting network structures within linear programs can lead to considerable improvement of the computational
solution of large-scale linear programming problems. A linear program is said to contain an embedded network structure provided
that some subset of its constraints can be interpreted as specifying conservation of flow. If a column of the constraint matrix
has at most two non-zeros, then it leads to embedded generalized network structure and if these non-zeros are unit elements
and of opposite signs, then it leads to embedded pure network structure.
In this paper, we are concerned with algorithms for detecting embedded pure network structures within linear programs. The
network extraction methods are presented in two groups. The first group covers deletion and addition based algorithms and
the second group covers GUB based algorithms. We have extended the GUB based algorithm appearing in the second group by introducing
Markowitz merit count approach for exploiting matrix non zeros. A set of well known test problems has been used to carry out
computational experiments which show that our extensions to the GUB based algorithms give better results than the algorithms
reported earlier. 相似文献
977.
978.
A theory of quaternion-valued hyperholomorphic functions (h.h.f.) is being developed which is closely related to the Maxwell equations for monochromatic electromagnetic fields. The main integral formulas are established, and some boundary-value properties are studied. 相似文献
979.
Robert McLachlan 《Numerische Mathematik》1993,66(1):465-492
Summary The numerical integration of a wide class of Hamiltonian partial differential equations by standard symplectic schemes is discussed, with a consistent, Hamiltonian approach. We discretize the Hamiltonian and the Poisson structure separately, then form the the resulting ODE's. The stability, accuracy, and dispersion of different explicit splitting methods are analyzed, and we give the circumstances under which the best results can be obtained; in particular, when the Hamiltonian can be split into linear and nonlinear terms. Many different treatments and examples are compared. 相似文献
980.
We prove that the space of spectral measures on a W*-algebra is a smooth Banach manifold in a natural way and that the action of the group of invertible elements of the algebra by inner automorphisms makes it into a reductive homogeneous space. This gives a geometric structure for the set of normal operators with the same spectrum. 相似文献