In this work, a new representation is developed for generalized hypergeometric functions of type p F p . To this end a first order vector differential equation is constructed in a way such that the derivative of the u...
详细信息
作者：
白中治State Key Laboratory of Scientific/Engineering Computing
Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 P.R. China
For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured preconditioners through matrix transformation and matrix approximations. For the specific versions such a...
详细信息
For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices. Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRES and restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two-by-two coefficient matrices. In particular, these structured preconditioners can lead to high-quality preconditioning matrices for some typical matrices from the real-world applications.
The teracluster LSSC-II installed at the State Key Laboratory of Scientific and engineeringcomputing, Chinese Academy of Sciences is one of the most powerful PC clusters in China. It has a peek performance of 2Tflops...
详细信息
The teracluster LSSC-II installed at the State Key Laboratory of Scientific and engineeringcomputing, Chinese Academy of Sciences is one of the most powerful PC clusters in China. It has a peek performance of 2Tflops. With a Linpack performance of 1.04Tflops, it is ranked at the 43rd place in the 20th TOP500 List (November 2002), 51st place in the 21st TOP500 List (June 2003), and the 82nd place in the 22nd TOP500 List (November 2003) with a new Linpack performance of 1.3Tflops. In this paper, we present some design principles of this cluster, as well as its applications in some large-scale numerical simulations.
Solving integral equations in high dimensions requires a huge computational effort and hence fast methods are desirable. We develop and analyze Boolean approximation methods using the piecewise constant functions for ...
详细信息
作者：
郭福奎张玉峰School of Information Science and Engineering
Shandong University of Science and TechnologyTaian 271019 School of Information Science and Engineering
Shandong University of Science and TechnologyTaian 271019 Institute of Computational Mathematics and Scientific Engineering ComputingAcademia SinicaBeijing 100080 new loop algebra and a new Lax pair are constructed respectively. It follows that the integrable coupling of the TC hierarchy of equations which is also an expanding integrable model is obtained. Specially the integrable coupling of the famous KdV equation is presented.
A new loop algebra and a new Lax pair are constructed, respectively. It follows that the integrable coupling of the TC hierarchy of equations, which is also an expanding integrable model, is obtained. Specially, the i...
详细信息
A new loop algebra and a new Lax pair are constructed, respectively. It follows that the integrable coupling of the TC hierarchy of equations, which is also an expanding integrable model, is obtained. Specially, the integrable coupling of the famous KdV equation is presented.
Conjugate gradient methods are very important ones for solving nonlinear optimization problems,especially for large scale problems. However, unlike quasi-Newton methods, conjugate gradient methods wereusually analyzed...
详细信息
Conjugate gradient methods are very important ones for solving nonlinear optimization problems,especially for large scale problems. However, unlike quasi-Newton methods, conjugate gradient methods wereusually analyzed individually. In this paper, we propose a class of conjugate gradient methods, which can beregarded as some kind of convex combination of the Fletcher-Reeves method and the method proposed byDai et al. To analyze this class of methods, we introduce some unified tools that concern a general methodwith the scalarβk having the form of φk/φk-1. Consequently, the class of conjugate gradient methods canuniformly be analyzed.
Trust region (TR) algorithms are a class of recently developed algorithms for nonlinear optimization. A new family of TR algorithms for unconstrained optimization, which is the extension of the usual TR method, is pre...
详细信息
Trust region (TR) algorithms are a class of recently developed algorithms for nonlinear optimization. A new family of TR algorithms for unconstrained optimization, which is the extension of the usual TR method, is presented in this paper. When the objective function is bounded below and continuously, differentiable, and the norm of the Hesse approximations increases at most linearly with the iteration number, we prove the global convergence of the algorithms. Limited numerical results are reported, which indicate that our new TR algorithm is competitive.
In this paper we propose a self-adaptive trust region algorithm. The trust region radius is updated at a variable rate according to the ratio between the actual reduction and the predicted reduction of the objective f...
详细信息
In this paper we propose a self-adaptive trust region algorithm. The trust region radius is updated at a variable rate according to the ratio between the actual reduction and the predicted reduction of the objective function, rather than by simply enlarging or reducing the original trust region radius at a constant rate. We show that this new algorithm preserves the strong convergence property of traditional trust region methods. Numerical results are also presented.
Linear systems associated with numerical methods for constrained optimization are discussed in this paper. It is shown that the corresponding subproblems arise in most well-known methods, no matter line search methods...
详细信息
Linear systems associated with numerical methods for constrained optimization are discussed in this paper. It is shown that the corresponding subproblems arise in most well-known methods, no matter line search methods or trust region methods for constrained optimization can be expressed as similar systems of linear equations. All these linear systems can be viewed as some kinds of approximation to the linear system derived by the Lagrange-Newton method. Some properties of these linear systems are analyzed.
The homogeneous balance method is a method for solving general partial differential equations (PDEs). Inthis paper we solve a kind of initial problems of the PDEs by using the special Backlund transformations of the i...
详细信息
The homogeneous balance method is a method for solving general partial differential equations (PDEs). Inthis paper we solve a kind of initial problems of the PDEs by using the special Backlund transformations of the initialproblem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initialproblems of Nizhnich and the Nizhnich-Novikov-Veselov equations are solved by using this approach.
暂无评论