共查询到20条相似文献,搜索用时 31 毫秒
1.
For any real matrix A, this paper is concerned with the estimation of the spectral radius of A. The relationship between the weighted norm and the discrete Lyapunov equation of the matrix A is obtained. On the basis of the relationship, an iterative algorithm is presented to obtain the spectral radius of A and to estimate the solution of the corresponding linear discrete system. Several numerical examples are given to show that the iterative algorithm is effective. 相似文献
2.
In this paper, an iterative algorithm is constructed for solving linear matrix equation AXB = C over generalized centro-symmetric matrix X. We show that, by this algorithm, a solution or the least-norm solution of the matrix equation AXB = C can be obtained within finite iteration steps in the absence of roundoff errors; we also obtain the optimal approximation
solution to a given matrix X
0 in the solution set of which. In addition, given numerical examples show that the iterative method is efficient. 相似文献
3.
A symmetrizer of the matrix A is a symmetric solution X that satisfies the matrix equation XA=AX. An exact matrix symmetrizer is computed by obtaining a general algorithm and superimposing a modified multiple modulus residue arithmetic on this algorithm. A procedure based on computing a symmetrizer to obtain a symmetric matrix, called here an equivalent symmetric matrix, whose eigenvalues are the same as those of a given real nonsymmetric matrix is presented.Supported by CSIR. 相似文献
4.
Geurt Jongbloed 《Journal of computational and graphical statistics》2013,22(3):310-321
Abstract The problem of minimizing a smooth convex function over a specific cone in IRn is frequently encountered in nonparametric statistics. For that type of problem we suggest an algorithm and show that this algorithm converges to the solution of the minimization problem. Moreover, a simulation study is presented, showing the superiority of our algorithm compared to the EM algorithm in the interval censoring case 2 setting. 相似文献
5.
We show that any solution of the two-dimensional Navier-Stokes equation whose vorticity distribution is uniformly bounded in L1(R2) for positive times is entirely determined by the trace of the vorticity at t=0, which is a finite measure. When combined with previous existence results by Cottet, by Giga, Miyakawa & Osada, and by Kato, this uniqueness property implies that the Cauchy problem for the vorticity equation in R2 is globally well-posed in the space of finite measures. In particular, this provides an example of a situation where the Navier-Stokes equation is well-posed for arbitrary data in a function space that is large enough to contain the initial data of some self-similar solutions. 相似文献
6.
Cristina Flaut 《Journal of Difference Equations and Applications》2013,19(7):905-920
ABSTRACTIn this paper, we present some applications of a difference equation of degree k. Using such an equation, we provide an algorithm for messages encryption and decryption. Moreover, by using the matrix associated to a difference equation of degree k, we present an application in Coding Theory. 相似文献
7.
In this paper we develop approximation algorithms for two-stage convex chance constrained problems. Nemirovski and Shapiro
(Probab Randomized Methods Des Uncertain 2004) formulated this class of problems and proposed an ellipsoid-like iterative
algorithm for the special case where the impact function f (x, h) is bi-affine. We show that this algorithm extends to bi-convex f (x, h) in a fairly straightforward fashion. The complexity of the solution algorithm as well as the quality of its output are functions
of the radius r of the largest Euclidean ball that can be inscribed in the polytope defined by a random set of linear inequalities generated
by the algorithm (Nemirovski and Shapiro in Probab Randomized Methods Des Uncertain 2004). Since the polytope determining
r is random, computing r is difficult. Yet, the solution algorithm requires r as an input. In this paper we provide some guidance for selecting r. We show that the largest value of r is determined by the degree of robust feasibility of the two-stage chance constrained problem—the more robust the problem,
the higher one can set the parameter r. Next, we formulate ambiguous two-stage chance constrained problems. In this formulation, the random variables defining the
chance constraint are known to have a fixed distribution; however, the decision maker is only able to estimate this distribution
to within some error. We construct an algorithm that solves the ambiguous two-stage chance constrained problem when the impact
function f (x, h) is bi-affine and the extreme points of a certain “dual” polytope are known explicitly.
Research partially supported by NSF grants CCR-00-09972, DMS-01-04282 and ONR grant N000140310514. 相似文献
8.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(8):1206-1248
ABSTRACTWe propose a non-linear forward Feynman-Kac type equation, which represents the solution of a nonconservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that type of equation can be approached via a weighted particle system. 相似文献
9.
Yoshiki Otobe 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):489-516
We consider a time evolution of random fields with non-negative values on the real line. Such evolution is described by an infinite dimensional stochastic differential equation of Skorokhod's type, which is a stochastic partial differential equation (SPDE) of parabolic type with reflection. We shall show the existence of the solution, and its uniqueness when the diffusion coefficient is constant. 相似文献
10.
Nonconvergence of the plain Newton-min algorithm for linear complementarity problems with a P-matrix
The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) can be viewed as a semismooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x, Mx + q) = 0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge in at most n iterations. We show in this paper that this result no longer holds when M is a P-matrix of order ≥ 3, since then the algorithm may cycle. P-matrices are interesting since they are those ensuring the existence and uniqueness of the solution to the LCP for an arbitrary q. Incidentally, convergence occurs for a P-matrix of order 1 or 2. 相似文献
11.
ABSTRACT We consider a reaction-diffusion equation of bistable type in a square cylinder whose diameter varies with Neumann boundary conditions in dimension 2 and 3. We prove the nonexistence of generalized traveling wave solution of this equation when the diameter is suddenly strongly increased. At the same time, we prove that the solution of the equation with an exponentially decreasing initial condition cannot pass over a certain threshold far enough in the direction of propagation. The proof is divided in two steps. First, we extend the solution in the cylinder to a solution of the same equation in the half space. Then we overestimate it using Green's functions. 相似文献
12.
ABSTRACTA class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays. 相似文献
13.
Tadahisa Funaki 《Probability Theory and Related Fields》1991,90(4):519-562
Summary As a microscopic model we consider a system of interacting continuum like spin field overR
d
. Its evolution law is determined by the Ginzburg-Landau type random Hamiltonian and the total spin of the system is preserved by this evolution. We show that the spin field converges, under the hydrodynamic space-time scalling, to a deterministic limit which is a solution of a certain nonlinear diffusion equation. This equation describes the time evolution of the macroscopic field. The hydrodynamic scaling has an effect of the homogenization on the system at the same time. 相似文献
14.
Peter E. Caines Daniel Ho 《Stochastics An International Journal of Probability and Stochastic Processes》2020,92(4):642-657
ABSTRACT The density evolution of McKean–Vlasov stochastic differential equations in the presence of an absorbing boundary is analysed where the solution to such equations corresponds to the dynamics of partially killed large populations. By using a fixed point theorem, we show that the density evolution is characterized as the solution of an integro-differential Fokker–Planck equation with Cauchy–Dirichlet data. This problem arises naturally within mean field game theory. 相似文献
15.
Summary. We consider a piecewise constant finite element approximation to the convolution Volterra equation problem of the second
kind: find such that in a time interval . An a posteriori estimate of the error measured in the norm is developed and used to provide a time step selection criterion for an adaptive solution algorithm. Numerical examples
are given for problems in which is of a form typical in viscoelasticity theory.
Received March 5, 1998 / Revised version received November 30, 1998 / Published online December 6, 1999 相似文献
16.
Mourad E. H. Ismail 《Journal of Difference Equations and Applications》2020,26(4):488-509
ABSTRACTWe introduce a finite difference and q-difference analogues of the Asymptotic Iteration Method of Ciftci, Hall, and Saad. We give necessary, and sufficient condition for the existence of a polynomial solution to a general linear second-order difference or q-difference equation subject to a ‘terminating condition’, which is precisely defined. When a difference or q-difference equation has a polynomial solution, we show how to find the second solution. 相似文献
17.
In this article, we derive the exact rate of convergence of some approximation schemes associated to scalar stochastic differential
equations driven by a fractional Brownian motion with Hurst index H. We consider two cases. If H>1/2, the exact rate of convergence of the Euler scheme is determined. We show that the error of the Euler scheme converges
almost surely to a random variable, which in particular depends on the Malliavin derivative of the solution. This result extends
those contained in J. Complex. 22(4), 459–474, 2006 and C.R. Acad. Sci. Paris, Ser. I 340(8), 611–614, 2005. When 1/6<H<1/2, the exact rate of convergence of the Crank-Nicholson scheme is determined for a particular equation. Here we show convergence
in law of the error to a random variable, which depends on the solution of the equation and an independent Gaussian random
variable. 相似文献
18.
The following delay integral equationhas been proposed by Cooke and Kaplan to describe the spread of certain infectious diseases with periodic contact rate that varies seasonally. This mathematical model can also be interpreted as an evolution equation of a single species population. The purpose of this paper is to present an approximating algorithm for the continuous positive solution of this integral equation from the theory of epidemics. This algorithm is obtained by applying the successive approximations method and the rectangle formula, used for the calculation of the approximate value of integrals which appear in the right-hand-side of the terms of the sequence of successive approximations. In order to establish this approximating algorithm, we will suppose that this integral equation has a unique solution. The main result contains also the error of approximation of the solution obtained by applying this approximating algorithm.
相似文献
$ x(t)=\int\limits_{t-\tau}^{t}f(s,x(s))ds,\quad t\in \mathbb{R}, $
19.
Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints
Pham 《Applied Mathematics and Optimization》2008,46(1):55-78
Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility
and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as
a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value
function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a
stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear
equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation.
This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate
our results with several examples of stochastic volatility models popular in the financial literature. 相似文献
20.
《随机分析与应用》2013,31(5):903-920
Abstract A limiting problem for a stochastic evolution equation is studied in the paper. In the equation, the linear operator is non-positive with a pure point spectrum, the non-linearity is monotone, and the Brownian motion is cylindrical. It is shown that, in the limit, the mild solution to the evolution equation tends to the solution of an ordinary Ito equation. 相似文献