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991.
This paper is concerned with the efficient solution of the linear systems of equations that arise from an adaptive space-implicit
time discretisation of the Black-Scholes equation. These nonsymmetric systems are very large and sparse, so an iterative method
will usually be the method of choice. However, such a method may require a large number of iterations to converge, particularly
when the timestep used is large (which is often the case towards the end of a simulation which uses adaptive timestepping).
An appropriate preconditioner is therefore desirable. In this paper we show that a very simple multigrid algorithm with standard
components works well as a preconditioner for these problems. We analyse the eigenvalue spectrum of the multigrid iteration
matrix for uniform grid problems and illustrate the method’s efficiency in practice by considering the results of numerical
experiments on both uniform grids and those which use adaptivity in space. 相似文献
992.
Vakhid Masagutov 《Arkiv f?r Matematik》2011,49(1):129-148
We prove that every homomorphism \(\mathcal{O}^{E}_{\zeta}\rightarrow\mathcal{O}^{F}_{\zeta}\), with E and F Banach spaces and ζ∈? m , is induced by a \(\mathop{\mathrm{Hom}}(E,F)\)-valued holomorphic germ, provided that 1≤m<∞. A similar structure theorem is obtained for the homomorphisms of type \(\mathcal{O}^{E}_{\zeta}\rightarrow\mathcal{S}_{\zeta}\), where \(\mathcal{S}_{\zeta}\) is a stalk of a coherent sheaf of positive depth. We later extend these results to sheaf homomorphisms, obtaining a condition on coherent sheaves which guarantees the sheaf to be equipped with a unique analytic structure in the sense of Lempert–Patyi. 相似文献
993.
The set of all m × n Boolean matrices is denoted by $
\mathbb{M}
$
\mathbb{M}
m,n
. We call a matrix A ∈ $
\mathbb{M}
$
\mathbb{M}
m,n
regular if there is a matrix G ∈ $
\mathbb{M}
$
\mathbb{M}
n,m
such that AGA = A. In this paper, we study the problem of characterizing linear operators on $
\mathbb{M}
$
\mathbb{M}
m,n
that strongly preserve regular matrices. Consequently, we obtain that if min{m, n} ⩽ 2, then all operators on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserve regular matrices, and if min{m, n} ⩾ 3, then an operator T on $
\mathbb{M}
$
\mathbb{M}
m,n
strongly preserves regular matrices if and only if there are invertible matrices U and V such that T(X) = UXV for all X ε $
\mathbb{M}
$
\mathbb{M}
m,n
, or m = n and T(X) = UX
T
V for all X ∈ $
\mathbb{M}
$
\mathbb{M}
n
. 相似文献
994.
David F. Anderson Scott T. Chapman Nathan Kaplan Desmond Torkornoo 《Semigroup Forum》2011,82(1):96-108
Let M be a commutative, cancellative, atomic monoid and x a nonunit in M. We define ω(x)=n if n is the smallest positive integer with the property that whenever x∣a 1???a t , where each a i is an atom, there is a T?{1,2,…,t} with |T|≤n such that x∣∏k∈T a k . The ω-function measures how far x is from being prime in M. In this paper, we give an algorithm for computing ω(x) in any numerical monoid. Simple formulas for ω(x) are given for numerical monoids of the form 〈n,n+1,…,2n?1〉, where n≥3, and 〈n,n+1,…,2n?2〉, where n≥4. The paper then focuses on the special case of 2-generator numerical monoids. We give a formula for computing ω(x) in this case and also necessary and sufficient conditions for determining when x is an atom. Finally, we analyze the asymptotic behavior of ω(x) by computing \(\lim_{x\rightarrow \infty}\frac{\omega(x)}{x}\). 相似文献
995.
The existence and uniqueness of the global solution of stochastic differential equations with discrete variable delay is investigated
in this paper, and the pathwise estimation is also done by using Lyapunov function method and exponential martingale inequality.
The results can be used not only in the case of bounded delay but also in the case of unbounded delay. As the applications,
this paper considers the pathwise estimation of solutions of stochastic pantograph equations. 相似文献
996.
A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed.In this method,linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved.The numerical results show that the new method may be capable of processing some large scale problems. 相似文献
997.
Yong-jiang Guo 《应用数学学报(英文版)》2011,27(1):43-58
A GI/G/1 queue with vacations is considered in this paper.We develop an approximating technique on max function of independent and identically distributed(i.i.d.) random variables,that is max{ηi,1 ≤ i ≤ n}.The approximating technique is used to obtain the fluid approximation for the queue length,workload and busy time processes.Furthermore,under uniform topology,if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate,we prove by the... 相似文献
998.
Iosif Pinelis 《Journal of Theoretical Probability》2011,24(2):409-421
Integral expressions for positive-part moments E X+pmathsf{E},X_{+}^{p} (p>0) of random variables X are presented, in terms of the Fourier–Laplace or Fourier transforms of the distribution of X. A necessary and sufficient condition for the validity of such an expression is given. This study was motivated by extremal problems in probability and statistics, where one needs to evaluate such positive-part moments. 相似文献
999.
We present branching-on-hyperplane methods for solving mixed integer linear and mixed integer convex programs. In particular,
we formulate the problem of finding a good branching hyperplane using a novel concept of adjoint lattice. We also reformulate
the problem of rounding a continuous solution to a mixed integer solution. A worst case complexity of a Lenstra-type algorithm
is established using an approximate log-barrier center to obtain an ellipsoidal rounding of the feasible set. The results
for the mixed integer convex programming also establish a complexity result for the mixed integer second order cone programming
and mixed integer semidefinite programming feasibility problems as a special case. Our results motivate an alternative reformulation
technique and a branching heuristic using a generalized (e.g., ellipsoidal) norm reduced basis available at the root node. 相似文献
1000.
Khakim D. Ikramov 《Computational Mathematics and Mathematical Physics》2011,51(4):505-512
Suppose that one should verify whether a given complex n × n matrix can be converted into a real matrix by a unitary similarity transformation. Sufficient conditions for this property
to hold were found in an earlier publication of this author. These conditions are relaxed in the following way: as before,
the spectrum is required to be simple, but pairs of complex conjugate eigenvalues $
\lambda ,\bar \lambda
$
\lambda ,\bar \lambda
are now allowed. However, the eigenvectors corresponding to such eigenvalues must not be orthogonal. 相似文献