共查询到20条相似文献,搜索用时 62 毫秒
1.
M. Brokate 《Numerische Mathematik》1985,46(1):85-99
Summary For a free boundary problem for a linear hyperbolic system in one space dimension with two unknowns we discuss a numerical algorithm which combines the method of characteristics and the front tracking method. We prove quadratic resp. linear convergence and illustrate this with numerical examples. 相似文献
2.
F. Locher 《Numerische Mathematik》1980,34(2):99-109
Summary As a generalisation of divided differences we consider linear functionals vanishing for polynomials of given degree and with discrete support. It is shown that functionals of that type may be uniquely represented by a linear combination of divided differences. On the basis of this representation theorem we introduce the concept of positivity and definiteness of functions and linear functionals. Next we show that in many cases positivity follows from the number of sign changes of the coefficients of the given linear functional. These results may be applied to the problems of nonexistence of Newton-Côtes and Gegenbauer quadrature formulas with positive weights and to the monotony problem of Gauss and Newton Côtes quadrature. 相似文献
3.
The problem of estimating the precision matrix of a multivariate normal distribution model is considered with respect to a quadratic loss function. A number of covariance estimators originally intended for a variety of loss functions are adapted so as to obtain alternative estimators of the precision matrix. It is shown that the alternative estimators have analytically smaller risks than the unbiased estimator of the precision matrix. Through numerical studies of risk values, it is shown that the new estimators have substantial reduction in risk. In addition, we consider the problem of the estimation of discriminant coefficients, which arises in linear discriminant analysis when Fisher's linear discriminant function is viewed as the posterior log-odds under the assumption that two classes differ in mean but have a common covariance matrix. The above method is also adapted for this problem in order to obtain improved estimators of the discriminant coefficients under the quadratic loss function. Furthermore, a numerical study is undertaken to compare the properties of a collection of alternatives to the “unbiased” estimator of the discriminant coefficients. 相似文献
4.
Werner Sautter 《Numerische Mathematik》1984,44(1):139-152
Summary F.L. Bauer has treated in several papers [1, 3, 4] the condition related to the solution of linear equations and to the algebraic eigenvalue problem. We study the condition for the linear least squares problem with linear equality constraints (problem LSE). A perturbation theory of problem LSE is presented and three condition numbers are defined. Problem LSE includes the linear least squares problem (problem LS). There are examples with identical solution of problem LSE and of problem LS. Sometimes the condition of problem LSE is better and sometimes the condition of problem LS is better. Several numerical tests illustrate the theory.
Herrn Prof. Dr. Dr. F.L. Bauer zum 60. Geburtstag gewidmet 相似文献
5.
《Optimization》2012,61(4):525-533
In the paper the problem of existence of optimal control is considered for a control problem with a linear elliptic equation whose coefficients depend on the control. 相似文献
6.
In the present paper, we obtain the two-scale limit system of a sequence of linear elliptic periodic problems with varying coefficients. We show that this system has not the same structure than the classical one, obtained when the coefficients are fixed. This is due to the apparition of nonlocal effects. Our results give an example showing that the homogenization of elliptic problems with varying coefficients, depending on one parameter, gives in general a nonlocal limit problem. 相似文献
7.
Summary In this paper we study linear stationary iterative methods with nonnegative iteration matrices for solving singular and consistent systems of linear equationsAx=b. The iteration matrices for the schemes are obtained via regular and weak regular splittings of the coefficients matrixA. In certain cases when only some necessary, but not sufficient, conditions for the convergence of the iterations schemes exist, we consider a transformation on the iteration matrices and obtain new iterative schemes which ensure convergence to a solution toAx=b. This transformation is parameter-dependent, and in the case where all the eigenvalues of the iteration matrix are real, we show how to choose this parameter so that the asymptotic convergence rate of the new schemes is optimal. Finally, some applications to the problem of computing the stationary distribution vector for a finite homogeneous ergodic Markov chain are discussed.Research sponsored in part by US Army Research Office 相似文献
8.
Houde Han 《Numerische Mathematik》1994,68(2):269-281
Summary.
In this paper, we mainly consider the three dimensional Neumann
problem in
linear elasticity, which is reduced to a system of integro-differential
equations on the boundary based on a new representation of
the derivatives of
the double-layer potential. Furthermore a new boundary finite element
method
for this Neumann problem is presented.
Received July 13, 1992 / Revised version received June 28, 1993 相似文献
9.
On one approach to a posteriori error estimates for evolution problems solved by the method of lines 总被引:2,自引:0,他引:2
Summary. In this paper, we describe a new technique for a posteriori error estimates suitable to parabolic and hyperbolic equations
solved by the method of lines. One of our goals is to apply known estimates derived for elliptic problems to evolution equations.
We apply the new technique to three distinct problems: a general nonlinear parabolic problem with a strongly monotonic elliptic
operator, a linear nonstationary convection-diffusion problem, and a linear second order hyperbolic problem. The error is
measured with the aid of the -norm in the space-time cylinder combined with a special time-weighted energy norm. Theory as well as computational results
are presented.
Received September 2, 1999 / Revised version received March 6, 2000 / Published online March 20, 2001 相似文献
10.
Summary In his fundamental paper on general fixed-stepsize methods, Skeel [6] studied convergence properties, but left the existence of asymptotic expansions as an open problem. In this paper we give a complete answer to this question. For the special cases of one-step and linear multistep methods our proof is shorter than the published ones.Asymptotic expansions are the theoretical base for extrapolation methods. 相似文献
11.
Summary.
We analyze the convergence of a substructuring iterative method
with Lagrange multipliers, proposed recently by Farhat and Roux.
The method decomposes finite element
discretization of an elliptic boundary value problem into
Neumann problems on the subdomains plus a coarse problem for the
subdomain nullspace components. For linear conforming elements and
preconditioning by the Dirichlet problems on the subdomains,
we prove the asymptotic bound on the condition number
,
or ,where
is the characteristic element size and
subdomain size.
Received January 3, 1995 相似文献
12.
费威 《数学的实践与认识》2012,42(20)
针对线性规划对偶问题最优解不唯一时,在已有文献提出的对偶最优解不唯一的充要条件定理基础上,结合线性规划灵敏度分析,提出影子价格的求解判断的简单准则及其命题,并进行证明.最后,用算例加以分析,指出该判断方法简单易行,也可作为通过计算软件求解影子价格的准确判断方法. 相似文献
13.
Alastair Spence 《Numerische Mathematik》1978,29(2):133-147
Summary Approximate solutions of the linear integral equation eigenvalue problem can be obtained by the replacement of the integral by a numerical quadrature formula and then collocation to obtain a linear algebraic eigenvalue problem. This method is often called the Nyström method and its convergence was discussed in [7]. In this paper computable error bounds and dominant error terms are derived for the approximation of simple eigenvalues of nonsymmetric kernels. 相似文献
14.
Luisa Donatella Marini 《Numerische Mathematik》1987,50(5):533-545
Summary The computation of the homogenized coefficients involves the solution of a minimum problem for a quadratic functional. The use of conforming finite elements provides estimates from above. In this paper we prove that, under realistic assumptions, the use of linear non-conforming finite elements provides estimates from below. Hence, a-posteriori error estimates for the homogenized coefficients can be obtained. 相似文献
15.
16.
Summary. A model for the phase separation of a multi-component alloy with non-smooth free energy is considered. An error bound is
proved for a fully practical piecewise linear finite element approximation using a backward Euler time discretization. An
iterative scheme for solving the resulting nonlinear algebraic system is analysed. Finally numerical experiments with three
components in one and two space dimensions are presented. In the one dimensional case we compare some steady states obtained
numerically with the corresponding stationary solutions of the continuous problem, which we construct explicitly.
Received September 28, 1995 / Revised version received May 6, 1996 相似文献
17.
Nikolai Yu. Bakaev 《Numerische Mathematik》2002,92(4):621-651
Summary. We consider fully discrete approximations to a parabolic initial-boundary value problem with rough or distribution-valued
initial data in two space dimensions. For discretization in time and space, we apply single step methods and the standard
Galerkin method with piecewise linear test functions, respectively. For spatial discretization of the initial condition, we
are however forced to use more involved constructions. Our main result is stability and error estimates of the discrete solutions.
Received October 21, 1999 / Revised version received May 3, 2001 / Published online December 18, 2001 相似文献
18.
Summary. In this paper we study the numerical behaviour of elliptic
problems in which a small parameter is involved and an example
concerning the computation of elastic arches is analyzed using this
mathematical framework. At first, the statements of the problem and its
Galerkin approximations are defined and an asymptotic
analysis is performed. Then we give general conditions ensuring that
a numerical scheme will converge uniformly with respect to the small
parameter. Finally we study an example in
computation of arches working in linear elasticity conditions. We build one
finite element scheme giving a locking behaviour, and another one
which does not.
Revised version received October 25, 1993 相似文献
19.
A multicriteria competitive Markov decision process 总被引:1,自引:0,他引:1
A. M. Rodrı´guez-Chı´a J. Puerto F. R. Fernández 《Mathematical Methods of Operations Research》2002,55(3):359-369
20.
Summary. In this paper we establish two new projection-type methods for the solution of monotone linear complementarity problem (LCP).
The methods are a combination of the extragradient method and the Newton method, in which the active set strategy is used
and only one linear system of equations with lower dimension is solved at each iteration. It is shown that under the assumption
of monotonicity, these two methods are globally and linearly convergent. Furthermore, under a nondegeneracy condition they
have a finite termination property. At last, the methods are extended to solving monotone affine variational inequality problem.
Received October 10, 2000 / Revised version received May 22, 2001 / Published online October 17, 2001 相似文献