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1.
This paper is concerned with the numerical solution of a Karush–Kuhn–Tucker system. Such symmetric indefinite system arises
when we solve a nonlinear programming problem by an Interior-Point (IP) approach. In this framework, we discuss the effectiveness
of two inner iterative solvers: the method of multipliers and the preconditioned conjugate gradient method. We discuss the
implementation details of these algorithms in an IP scheme and we report the results of a numerical comparison on a set of
large scale test-problems arising from the discretization of elliptic control problems.
This research was supported by the Italian Ministry for Education, University and Research (MIUR), FIRB Project RBAU01JYPN. 相似文献
2.
Summary. In this paper, the adaptive filtering method is introduced and analysed. This method leads to robust algorithms for the solution
of systems of linear equations which arise from the discretisation of partial differential equations with strongly varying
coefficients. These iterative algorithms are based on the tangential frequency filtering decompositions (TFFD). During the
iteration with a preliminary preconditioner, the adaptive test vector method calculates new test vectors for the TFFD. The
adaptive test vector iterative method allows the combination of the tangential frequency decomposition and other iterative
methods such as multi-grid. The connection with the TFFD improves the robustness of these iterative methods with respect to
varying coefficients. Interface problems as well as problems with stochastically distributed properties are considered. Realistic
numerical experiments confirm the efficiency of the presented algorithms.
Received June 26, 1996 / Revised version received October 7, 1996 相似文献
3.
B. S. Goh 《Journal of Optimization Theory and Applications》1997,92(3):581-604
Existing algorithms for solving unconstrained optimization problems are generally only optimal in the short term. It is desirable to have algorithms which are long-term optimal. To achieve this, the problem of computing the minimum point of an unconstrained function is formulated as a sequence of optimal control problems. Some qualitative results are obtained from the optimal control analysis. These qualitative results are then used to construct a theoretical iterative method and a new continuous-time method for computing the minimum point of a nonlinear unconstrained function. New iterative algorithms which approximate the theoretical iterative method and the proposed continuous-time method are then established. For convergence analysis, it is useful to note that the numerical solution of an unconstrained optimization problem is none other than an inverse Lyapunov function problem. Convergence conditions for the proposed continuous-time method and iterative algorithms are established by using the Lyapunov function theorem. 相似文献
4.
《European Journal of Operational Research》2006,173(2):519-530
This paper applies algorithms integrating Integer Programming (IP) and Constraint Programming (CP) to the Mutually Orthogonal Latin Squares (MOLS) problem. We investigate the behaviour of these algorithms against traditional IP and CP schemes. Computational results are obtained with respect to various aspects of the algorithms, using instances of the 2 MOLS and 3 MOLS problems. The benefits of integrating IP with CP on this feasibility problem are clearly exhibited, especially in large problem instances. 相似文献
5.
Liviu Marin 《Numerical Methods for Partial Differential Equations》2012,28(3):899-925
We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over‐specified boundary in the case of the alternating iterative algorithm of Kozlov et al. (USSR Comput Math Math Phys 31 (1991), 45–52) applied to the Cauchy problem for the two‐dimensional modified Helmholtz equation. The two mixed, well‐posed and direct problems corresponding to every iteration of the numerical procedure are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is selected according to the generalized cross‐validation criterion. The iterative MFS algorithms with relaxation are tested for Cauchy problems associated with the modified Helmholtz equation in two‐dimensional geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the method. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
6.
本文研究了一类带误差的拟变分包含问题的迭代算法.利用黏性逼近法,获得了拟变分包含问题的迭代算法的强收敛结果,将最近一些文献的相应结果从迭代算法推广到带误差的迭代算法. 相似文献
7.
An iterative back substitution algorithm for the solution of tridiagonal matrix systems with fringes
《Journal of Computational and Applied Mathematics》2004,169(1):87-99
For tridiagonal matrix systems, a simple direct algorithm giving the solution exists, but in the most general case of tridiagonal matrix with fringes, the direct solving algorithms are more complicated. For big systems, direct methods are not well fitted and iterative algorithms are preferable. In this paper a relaxation type iterative algorithm is presented. It is an extension of the backward substitution method used for simple tridiagonal matrix systems. The performances show that this algorithm is a good compromise between a direct method and other iterative methods as block SOR. Its nature suggests its use as inner solver in the solution of problems derived by application of a decomposition domain method. A special emphasis is done on the programming aspect. The solving Fortran subroutines implementing the algorithm have been generated automatically from their specification by using a computer algebra system technique. 相似文献
8.
In this paper, by introducing a definition of parameterized comparison
matrix of a given complex square matrix, the solvability of a parameterized class
of complex nonsymmetric algebraic Riccati equations (NAREs) is discussed. The
existence and uniqueness of the extremal solutions of the NAREs is proved. Some
classical numerical methods can be applied to compute the extremal solutions of the
NAREs, mainly including the Schur method, the basic fixed-point iterative methods,
Newton's method and the doubling algorithms. Furthermore, the linear convergence
of the basic fixed-point iterative methods and the quadratic convergence of Newton's
method and the doubling algorithms are also shown. Moreover, some concrete parameter selection strategies in complex number field for the doubling algorithms
are also given. Numerical experiments demonstrate that our numerical methods are
effective. 相似文献
9.
Igor P. Boglaev 《Journal of Computational and Applied Mathematics》1997,80(2):680-316
This paper deals with iterative algorithms for domain decomposition applied to the solution of a quasilinear elliptic problem. Two iterative algorithms are examined: the first one is the Schwarz alternating procedure and the second algorithm is suitable for parallel computing. Convergence results are established in the two-domain and multidomain decomposition cases. Some issues of parallel implementation of these algorithms are discussed. 相似文献
10.
Under study is the problem of finding the nearest points from one ellipsoid to the other. Some new algorithms for solving this problem are constructed, using the theory of exact penalty functions and nonsmooth analysis. We propose two iterative methods of (steepest and hypodifferential) descent. The new algorithms (as compared with those previously known) have specific advantages; in particular, they are universal and less labor-consuming. Software for implementing these algorithms is developed inMATLAB and Maple. 相似文献
11.
Chuan-jn Xu 《计算数学(英文版)》1999,(4)
1.IntroductionDomaindecompositionmethodsareusefulapproximationtechniquestofacecomputationalfluiddynamicsproblems,especiallyincomplexphysicaldomainsandusingparallelcomputationalenvironments.Theyhavebeenfirstemployedinfinitedifferenceandfiniteelementme... 相似文献
12.
PARALLEL IMPLEMENTATIONS OF THE FAST SWEEPING METHOD 总被引:2,自引:0,他引:2
Hongkai Zhao 《计算数学(英文版)》2007,25(4):421-429
The fast sweeping method is an efficient iterative method for hyperbolic problems. It combines Gauss-Seidel iterations with alternating sweeping orderings. In this paper several parallel implementations of the fast sweeping method are presented. These parallel algorithms are simple and efficient due to the causality of the underlying partial different equations. Numerical examples are used to verify our algorithms. 相似文献
13.
H-非线性方程组的一种高效迭代解法 总被引:1,自引:0,他引:1
1.引言满足参见([5])(1.1)的任一非线性刚性函数f(y):所产生的非线性方程组称之为由 f(y)产生的 H-非线性方程组,其中 A,A1为与 f(y)的刚性无关的常数,最多为中等大小;的第i个特征值;常数,或者v>0且最多为中等大小;所谓“中等大小”是指与。相比较而言的;显然,已知;a,b,c,d满足且均为常数,(1.2)是由混合(Hybrid)法解初值问题导出的,其中 h是积分步长.对k1= 1,即所谓一阶刚性初值问题,混合法已有诸多研究(见[6,9-11,14-16]);对 k1= 2,即所… 相似文献
14.
Jian-Jun Zhang 《Applied mathematics and computation》2011,217(22):9380-9386
Recently, Ding and Chen [F. Ding, T. Chen, On iterative solutions of general coupled matrix equations, SIAM J. Control Optim. 44 (2006) 2269-2284] developed a gradient-based iterative method for solving a class of coupled Sylvester matrix equations. The basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified, so that the iterative solutions are obtained by applying hierarchical identification principle. In this note, by considering the coupled Sylvester matrix equation as a linear operator equation we give a natural way to derive this algorithm. We also propose some faster algorithms and present some numerical results. 相似文献
15.
A. V. Kalashnikov V. A. Kostenko 《Moscow University Computational Mathematics and Cybernetics》2008,32(3):177-181
Iterative multiprocessor scheduling algorithms are considered. The iterative algorithms make it possible to solve scheduling problems for a wide class of computer architectures but are very intricate from the computational point of view. To simplify the iterative algorithms, we propose an approach to their construction based on the subdivision of the space of correct schedules into disjoint domains, namely, an algorithm for constructing domains is proposed, the operations of the schedule transformations closed within the domains are introduced, and a technique for cutting off domains is developed. The approach developed also makes it possible to construct parallel algorithms with a low traffic of the exchange between parallel processes. 相似文献
16.
S. Amat J. A. Ezquerro M. A. Hernández‐Verón 《Numerical Linear Algebra with Applications》2015,22(4):585-595
The main goal of this paper is to approximate the principal pth root of a matrix by using a family of high‐order iterative methods. We analyse the semi‐local convergence and the speed of convergence of these methods. Concerning stability, it is well known that even the simplified Newton method is unstable. Despite it, we present stable versions of our family of algorithms. We test numerically the methods: we check the numerical robustness and stability by considering matrices that are close to be singular and badly conditioned. We find algorithms of the family with better numerical behavior than the Newton and the Halley methods. These two algorithms are basically the iterative methods proposed in the literature to solve this problem. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
17.
Numerical simulation is a common approach to understand many phenomena, usually yielding a computationally intensive problem. To overcome insufficient computer capacity and computational speed, a grid computing environment is a suitable approach. In this paper we focus on the development of parallel algorithms to solve a 3D transport model in such a context. The solver is based on the multisplitting Newton method that provides a coarse-grained scheme. Algorithms are implemented using JACE, a grid-enabled Java Asynchronous Computing Environment. This programming environment allows users to design synchronous and asynchronous parallel iterative algorithms as well. Experiments are carried out on a heterogeneous grid environment in which the behaviour of both parallel iterative algorithms is analysed. The results allow us to draw some conclusions about the use of the programming library JACE and the design of parallel iterative algorithms in a grid computing environment. 相似文献
18.
A. O. Savchenko V. P. Il’in D. S. Butyugin 《Journal of Applied and Industrial Mathematics》2016,10(2):277-287
We develop and experimentally study the algorithms for solving three-dimensionalmixed boundary value problems for the Laplace equation in unbounded domains. These algorithms are based on the combined use of the finite elementmethod and an integral representation of the solution in a homogeneous space. The proposed approach consists in the use of the Schwarz alternating method with consecutive solution of the interior and exterior boundary value problems in the intersecting subdomains on whose adjoining boundaries the iterated interface conditions are imposed. The convergence of the iterative method is proved. The convergence rate of the iterative process is studied analytically in the case when the subdomains are spherical layers with the known exact representations of all consecutive approximations. In this model case, the influence of the algorithm parameters on the method efficiency is analyzed. The approach under study is implemented for solving a problem with a sophisticated configuration of boundaries while using a high precision finite elementmethod to solve the interior boundary value problems. The convergence rate of the iterations and the achieved accuracy of the computations are illustrated with some numerical experiments. 相似文献
19.
20.
Four iterative algorithms (two of them new) for the evaluation of complex (Hopf) bifurcation points in ordinary differential equations are compared. A comparison of effectiveness of the proposed algorithms is made for two examples taken from chemical reaction engineering. The applicability of the algorithms for the solution of various types of problems is also discussed. 相似文献