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31.
Weighted FOM and GMRES for solving nonsymmetric linear systems 总被引:1,自引:0,他引:1
This paper presents two new methods called WFOM and WGMRES, which are variants of FOM and GMRES, for solving large and sparse
nonsymmetric linear systems. To accelerate the convergence, these new methods use a different inner product instead of the
Euclidean one. Furthermore, at each restart, a different inner product is chosen. The weighted Arnoldi process is introduced
for implementing these methods. After describing the weighted methods, we give the relations that link them to FOM and GMRES.
Experimental results are presented to show the good performances of the new methods compared to FOM(m) and GMRES(m).
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
32.
We consider the canonical descending and ascending central series of ideals of an associative algebra. In particular, we prove that some ideal in the descending central series is finite-dimensional if and only if some ideal in the ascending central series is finite-codimensional. This result is the associative algebra analogue of results due to Reinhold Baer and Philip Hall in group theory and Ian Stewart in Lie algebra. We also prove various related results. 相似文献
33.
S. Lajara 《Journal of Functional Analysis》2011,261(11):3211-3225
We show that for any probability measure μ there exists an equivalent norm on the space L1(μ) whose restriction to each reflexive subspace is uniformly smooth and uniformly convex, with modulus of convexity of power type 2. This renorming provides also an estimate for the corresponding modulus of smoothness of such subspaces. 相似文献
34.
B.Yousefi 《数学物理学报(B辑英文版)》2011,31(1):68-72
This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk. 相似文献
35.
This paper mainly concerns a tuple of multiplication operators
defined on the weighted and unweighted multi-variable Bergman
spaces, their joint reducing subspaces and the von Neumann algebra
generated by the orthogonal projections onto these subspaces. It is
found that the weights play an important role in the structures of
lattices of joint reducing subspaces and of associated von Neumann
algebras. Also, a class of special weights is taken into account.
Under a mild condition it is proved that if those multiplication
operators are defined by the same symbols, then the corresponding
von Neumann algebras are $*$-isomorphic to the one defined on the
unweighted Bergman space. 相似文献
36.
Alexander Barvinok 《Foundations of Computational Mathematics》2007,7(2):229-244
We consider the problem of efficient integration of an n-variate polynomial with respect to the Gaussian measure in ℝn and related problems of complex integration and optimization of a polynomial on the unit sphere. We identify a class of n-variate
polynomials f for which the integral of any positive integer power fp over the whole space is well approximated by a properly scaled integral over a random subspace of dimension O(log n). Consequently,
the maximum of f on the unit sphere is well approximated by a properly scaled maximum on the unit sphere in a random subspace
of dimension O(log n). We discuss connections with problems of combinatorial counting and applications to efficient approximation
of a hafnian of a positive matrix. 相似文献
37.
Guangjun Zhao 《Discrete Mathematics》2007,307(22):2861-2865
A new q-analogue of the sum of cubes is given with a combinatorial interpretation on the lattice of subspaces. 相似文献
38.
39.
The characteristic function has been an important tool for studying completely non-unitary contractions on Hilbert spaces.
In this note, we consider completely non-coisometric contractive tuples of commuting operators on a Hilbert space H. We show
that the characteristic function, which is now an operator-valued analytic function on the open Euclidean unit ball in ℂn, is a complete unitary invariant for such a tuple. We prove that the characteristic function satisfies a natural transformation
law under biholomorphic mappings of the unit ball. We also characterize all operator-valued analytic functions which arise
as characteristic functions of pure commuting contractive tuples. 相似文献
40.
L. P. Vlasov 《Mathematical Notes》1997,61(1):38-47
Functionals (vector measures) defined on the spaceC(Q, X) of continuous abstract functions (whereQ is a compact Hausdorff space andX is a Banach space) and attaining their norm on the unit sphere are considered. A characterization of such functionals is
given in terms of the Radon-Nikodym derivative of the vector measure with respect to the variation of the measure and in terms
of analogs of the derivative. Applications to the characterization of finite-codimensional subspaces with the best approximation
property are given. Similar results are obtained for the spaceB(Q, Σ, X) of uniform limits of simple functions.
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 45–56, January, 1997.
Translated by V. E. Nazaikinskii 相似文献