共查询到20条相似文献,搜索用时 15 毫秒
1.
Most factorization invariants in the literature extract extremal factorization behavior, such as the maximum and minimum factorization lengths. Invariants of intermediate size, such as the mean, median, and mode factorization lengths are more subtle. We use techniques from analysis and probability to describe the asymptotic behavior of these invariants. Surprisingly, the asymptotic median factorization length is described by a number that is usually irrational. 相似文献
2.
Terry A. Loring 《Expositiones Mathematicae》2012,30(3):250-267
We review known factorization results for quaternion matrices. Specifically, we derive the Jordan canonical form, polar decomposition, singular value decomposition, and QR factorization. We prove that there is a Schur factorization for commuting matrices, and from this derive the spectral theorem. We do not consider algorithms, but do point to some of the numerical literature. 相似文献
3.
D. Zangurashvili 《Applied Categorical Structures》2001,9(6):625-650
We present an approach to construct factorization systems in abstract categories. It gives new factorization systems from some given ones, when we have a relevant family of adjunctions between slice categories. The approach is based on the notion of a local factorization system, which is introduced in this paper. Relations between local factorization systems and full replete reflective subcategories of corresponding slice categories are investigated. Several applications of this approach are given. 相似文献
4.
Jiří Adámek Horst Herrlich Jiří Rosický Walter Tholen 《Applied Categorical Structures》2002,10(3):237-249
Weak factorization systems, important in homotopy theory, are related to injective objects in comma-categories. Our main result is that full functors and topological functors form a weak factorization system in the category of small categories, and that this is not cofibrantly generated. We also present a weak factorization system on the category of posets which is not cofibrantly generated. No such weak factorization systems were known until recently. This answers an open problem posed by M. Hovey. 相似文献
5.
We propose a new inertia‐revealing factorization for sparse symmetric matrices. The factorization scheme and the method for extracting the inertia from it were proposed in the 1960s for dense, banded, or tridiagonal matrices, but they have been abandoned in favor of faster methods. We show that this scheme can be applied to any sparse symmetric matrix and that the fill in the factorization is bounded by the fill in the sparse QR factorization of the same matrix (but is usually much smaller). We describe our serial proof‐of‐concept implementation and present experimental results, studying the method's numerical stability and performance. 相似文献
6.
V. B. Vasil'ev 《Mathematical Notes》2000,68(5-6):556-568
We introduce a definition of the wave factorization of symbols of elliptic pseudodifferential operators and demonstrate applications of the wave factorization to the analysis of pseudodifferential equations in cones. 相似文献
7.
We investigate canonical factorizations of ordered functors of ordered groupoids through star-surjective functors. Our main construction is a quotient ordered groupoid, depending on an ordered version of the notion of normal subgroupoid, that results in the factorization of an ordered functor as a star-surjective functor followed by a star-injective functor. Any star-injective functor possesses a universal factorization through a covering, by Ehresmann’s Maximum Enlargement Theorem. We also show that any ordered functor has a canonical factorization through a functor with the ordered homotopy lifting property. 相似文献
8.
Positivity - We show a factorization through Lorentz spaces for Banach-space-valued operators defined in Banach function spaces. Although our results are inspired in the classical factorization... 相似文献
9.
A. B. Shabat 《Theoretical and Mathematical Physics》2017,193(1):1420-1428
We consider a problem of factoring the scattering matrix for Schrödinger equation on the real axis. We find the elementary factorization blocks in both the finite and infinite cases and establish a relation to the matrix conjugation problem. We indicate a general scheme for constructing a large class of scattering matrices admitting a quasirational factorization. 相似文献
10.
In this paper, we propose a new factorization method for block tridiagonal symmetric indefinite matrices. We also discuss
the stability of the factorization method. As a measurement of stability, an effective condition number is derived by using
backward error analysis and perturbation analysis. It shows that under some suitable assumptions, the solution obtained by
this factorization method is acceptable. Numerical results demonstrate that the factorization is stable if its condition number
is not too large.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
11.
We propose a variant of parallel block incomplete factorization preconditioners for a symmetric block-tridiagonalH-matrix. Theoretical properties of these block preconditioners are compared with those of block incomplete factorization preconditioners
for the corresponding comparison matrix. Numerical results of the preconditioned CG(PCG) method using these block preconditioners
are compared with those of PCG using other types of block incomplete factorization preconditioners. Lastly, parallel computations
of the block incomplete factorization preconditioners are carried out on the Cray C90. 相似文献
12.
《Operations Research Letters》2014,42(1):58-63
This paper proposes a simple factorization property for the workload distribution of the BMAP/G/1/ vacation queues under variable service speed. The server provides service at different service speeds depending on the phases of the underlying Markov chain. Using the factorization principle, the workload distribution at any arbitrary time point can be easily derived only by obtaining the distribution during the idle period. We prove the factorization property and the moments formula. Lastly, we provide some applications of our factorization principle. 相似文献
13.
Gyula Lakos 《Linear algebra and its applications》2010,432(1):338-346
We generalize the Wiener-Hopf factorization of Laurent series to more general commutative coefficient rings, and we give explicit formulas for the decomposition. We emphasize the algebraic nature of this factorization. 相似文献
14.
This paper proposes a simple factorization principle that can be used efficiently and effectively to derive the vector generating
function of the queue length at an arbitrary time of the BMAP/G/1/ queueing systems under variable service speed. We first
prove the factorization property. Then we provide moments formula. Lastly we present some applications of the factorization
principle. 相似文献
15.
We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld (American Mathematical
Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004), to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and factorization
structures, in a sense analogous to Quillen’s homotopy theory of differential graded Lie algebras. We prove the equivalence
of higher-dimensional chiral and factorization algebras by embedding factorization algebras into a larger category of chiral
commutative coalgebras, then realizing this interrelation as a chiral form of Koszul duality. We apply these techniques to
rederive some fundamental results of Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American
Mathematical Society, Providence, RI, 2004) on chiral enveloping algebras of *{\star} -Lie algebras. 相似文献
16.
《Journal of Combinatorial Theory, Series B》1987,43(2):140-150
We show that any two cartesian factorizations of a connected graph have a strict common refinement, improving on the unique factorization theorem of G. Sabidussi. (The cartesian product is the product wherein two vertices are adjacent when they are adjacent in one coordinate and equal in all other coordinates.) Among the applications, we can deduce the strict refinement theorem for chain-finite posets, and (using a cartesian factorization algorithm of P. Winkler) we give a polynomial-time algorithm for cardinal factorization of connected finite posets. 相似文献
17.
We give criteria when a full subcategory D of the category of groups has C-universal factorization property (C-UFP) or C-strong universal factorization property(C-SUFP) for a certain category of groups C.As a byproduct,we give affirmative answers to three unsettled questions in[S.W.Kim,J.B.Lee,Universal factorization property of certain polycyclic groups,J.Pure Appl.Algebra 204 (2006) 555-567]. 相似文献
18.
Jae Heon Yun 《BIT Numerical Mathematics》2000,40(3):583-605
We propose block ILU (incomplete LU) factorization preconditioners for a nonsymmetric block-tridiagonal M-matrix whose computation can be done in parallel based on matrix blocks. Some theoretical properties for these block ILU factorization preconditioners are studied and then we describe how to construct them effectively for a special type of matrix. We also discuss a parallelization of the preconditioner solver step used in nonstationary iterative methods with the block ILU preconditioners. Numerical results of the right preconditioned BiCGSTAB method using the block ILU preconditioners are compared with those of the right preconditioned BiCGSTAB using a standard ILU factorization preconditioner to see how effective the block ILU preconditioners are. 相似文献
19.
We show in this paper that given any reduced, cancellative, torsion-free, atomic monoid, it is possible to construct a possibly non-atomic domain with atomic factorization structure isomorphic to the given monoid. This is significant, since atomic monoids are known to have more freedom in the factorization properties they may possess than atomic domains. This construction is motivated by the paper written by Coykendall and Zafrullah (2004) [5], in which a non-atomic domain was constructed with factorization structure isomorphic to a singly-generated monoid. 相似文献