检索结果-内蒙古大学图书馆

A WELL CONDITIONED CHECKSUM SCHEME FOR algorithmIC FAULT TOLERANCE

INTEGRATION-THE VLSI JOURNAL 1991年第1期12卷 21-32页

作者： BOLEY, DL LUK, FT CORNELL UNIV SCH ELECT ENGN ITHACA NY 14853 USA

The weighted checksum scheme has been proposed as a low-cost fault tolerant procedure for parallel matrix computations. To guarantee multiple error detection and correction, the chosen weight vectors must satisfy some very specific properties about linear independence. However, previous weight generating methods that fulfill the independence criteria have troubles with numerical overflow. We will present a new scheme that generates weight vectors via Chebyshev polynomials to meet the requirements about independence and to avoid the difficulties with overflow.

关键词： algorithm-BASED FAULT TOLERANCE CHEBYSHEV POLYNOMIALS lanczos algorithm BERLEKAMP-MASSEY algorithm

来源：评论

学校读者我要写书评

暂无评论

Gauss quadrature rules for a generalized hermite weight function

引用

APPLIED MATHEMATICS AND COMPUTATION 2006年第1期180卷 86-96页

作者： Hascelik, A. Ihsan Univ Gaziantep Dept Math TR-27310 Gaziantep Turkey

In this paper we give an algorithm for finding the coefficients in the three term recurrence relation for the polynomials orthogonal With respect to the weight function W(x) = vertical bar x - b vertical bar(2 alpha)exp[-(x + c)(2)] on R, where a, b, c is an element of R, 2 alpha > -1. The algorithm is based on the discretization technique proposed by Gautschi, with the lanczos algorithm. Using the coefficients obtained by this algorithm we construct the Gauss quadrature rules relative to the weight function W(x). To show the performance of the new algorithm we give some numerical examples. (c) 2006 Published by Elsevier Inc.

关键词： Gauss quadrature rules generalized hermite polynomials discrete orthogonal polynomials Gautschi-Stieltjes procedure lanczos algorithm

来源：评论

学校读者我要写书评

暂无评论

On large-scale diagonalization techniques for the Anderson model of localization

引用

SIAM JOURNAL ON SCIENTIFIC COMPUTING 2006年第3期28卷 963-983页

作者： Schenk, Olaf Bollhofer, Matthias Romer, Rudolf A. Univ Basel Dept Comp Sci CH-4056 Basel Switzerland Tech Univ Berlin Dept Math D-10623 Berlin Germany Univ Warwick Ctr Comp Sci Coventry CV4 7AL W Midlands England Univ Warwick Dept Phys Coventry CV4 7AL W Midlands England

We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for large-scale sparse real and symmetric indefinite matrices of the Anderson model of localization. We compare the lanczos algorithm in the 1987 implementation by Cullum and Willoughby with the shift-and-invert techniques in the implicitly restarted lanczos method and in the Jacobi-Davidson method. Our preconditioning approaches for the shift-and-invert symmetric indefinite linear system are based on maximum weighted matchings and algebraic multilevel incomplete LDLT factorizations. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques for the highly ill-conditioned symmetric indefinite Anderson matrices. We demonstrate the effectiveness and the numerical accuracy of these algorithms. Our numerical examples reveal that recent algebraic multilevel preconditioning solvers can accelerate the computation of a large-scale eigenvalue problem corresponding to the Anderson model of localization by several orders of magnitude.

关键词： Anderson model of localization large-scale eigenvalue problem lanczos algorithm JACOBI-DAVIDSON algorithm Cullum-Willoughby implementation symmetric indefinite matrix multilevel preconditioning maximum weighted matching

来源：评论

学校读者我要写书评

暂无评论

On large-scale diagonalization techniques for the Anderson model of localization

引用

SIAM REVIEW 2008年第1期50卷 91-112页

作者： Schenk, Olaf Bollhoefer, Matthias Roemer, Rudolf A. Univ Basel Dept Comp Sci CH-4056 Basel Switzerland Tech Univ Carolo Wilhelmina Braunschweig Inst Computat Math D-38106 Braunschweig Germany Univ Warwick Dept Phys Coventry CV4 7AL W Midlands England Univ Warwick Ctr Comp Sci Coventry CV4 7AL W Midlands England

We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely, the computation of a few interior eigenvalues and their associated eigenvectors for large-scale sparse real and symmetric indefinite matrices of the Anderson model of localization. We compare the lanczos algorithm in the 1987 implementation by Cullum and Willoughby with the shift-and-invert techniques ill the implicitly restarted lanczos method and in the Jacobi-Davidson method. Our preconditioning approaches for the shift-and-invert symmetric indefinite linear system are based on maximum weighted matchings and algebraic multilevel incomplete LDLT factorizations. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques for the highly ill-conditioned symmetric indefinite Anderson matrices. We demonstrate the effectiveness and the numerical accuracy of these algorithms. Our numerical examples reveal that recent algebraic multilevel preconditioning solvers can accelerate the computation of a large-scale eigenvalue problem corresponding to the Anderson model of localization by several orders of magnitude.

关键词： Anderson model of localization large-scale eigenvalue problem lanczos algorithm Jacobi-Davidson algorithm Cullum-Willoughby implementation symmetric indefinite matrix multilevel preconditioning maximum weighted matching

来源：评论

学校读者我要写书评

暂无评论

Computing rovibrational levels of polyatomic molecules with polyspherical coordinates and a contracted basis built with a K-independent vibrational primitive basis

引用

MOLECULAR PHYSICS 2013年第14-15期111卷 2320-2333页

作者： Wang, Xiao-Gang Carrington, Tucker, Jr. Queens Univ Dept Chem Kingston ON K7L 3N6 Canada

To compute the rovibrational spectrum of a molecule undergoing large amplitude motion it is important to use geometrically defined internal coordinates. In this paper, we use polar-type coordinates and a contracted basis of products of vibrational wavefunctions and symmetric top functions: |v >|JKM >. To facilitate computing matrix elements of the kinetic energy operator obtained when the molecule-fixed axes are attached to two of the vectors used to define the coordinates, it is common to use vibrational basis functions that depend on K, the quantum number for the molecule-fixed z component of the angular momentum. In this paper, we show that it is possible to use a |v >|JKM > basis and forgo the K-dependent primitive vibrational functions. Instead, we use a K-independent primitive basis that is an extension of the one employed in Mol. Phys. 110, 825, (2012) for triatomics. Using a K-independent primitive basis obviates the need to compute and store contracted vibrational bases for each K. First, we demonstrate that rovibrational levels of H2O2 computed with the primitive basis, and no contraction, are accurate. Second, using the contracted |v >|JKM > basis we compute J > 0 levels of CH3D. In both cases, we compute rovibrational levels with J values higher than those of levels calculated heretofore and for lower J there is satisfying agreement with previous calculations using K-dependent vibrational basis functions.

关键词： rovibrational spectroscopy contracted basis set lanczos algorithm

来源：评论

学校读者我要写书评

暂无评论

Numerical algorithms for undamped gyroscopic systems

引用

COMPUTERS & MATHEMATICS WITH APPLICATIONS 1999年第1期37卷 49-66页

作者： Ferng, WR Lin, WW Wang, CS Natl Chiao Tung Univ Dept Appl Math Hsinchu Taiwan Natl Chiao Tung Univ Dept Math Hsinchu Taiwan Natl Cheng Kung Univ Dept Math Tainan 70101 Taiwan

The solutions of a gyroscopic vibrating system oscillating about an equilibrium position, with no external applied forces and no damping forces, are completely determined by the quadratic eigenvalue problem (-lambda(i)(2)M + lambda(i)G + K)x(i) = 0, for i = 1, ..., 2n, where M, G, and K are real n x n matrices, and M is symmetric positive definite (denoted by M > 0), G is skew symmetric, and either K > 0 or -K > 0. Gyroscopic systemin motion about a stable equilibrium position (with -K > 0) are well understood. Two lanczos-type algorithms, the pseudo skew symmetric lanczos algorithm and the J-lanczos algorithm, are studied for computing some extreme eigenpairs for solving gyroscopic systems in motion about an unstable equilibrium position (with K > 0). Shift and invert strategies, error bounds, implementation issues, and numerical results for both algorithms are presented in details. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： gyroscopic system lanczos algorithm Hamiltonian matrix quadratic eigenvalue problem generalized eigenvalue problem

来源：评论

学校读者我要写书评

暂无评论

Convergence of polynomial restart Krylov methods for eigenvalue computations

引用

SIAM REVIEW 2005年第3期47卷 492-515页

作者： Beattie, CA Embree, M Sorensen, DC Virginia Polytech Inst & State Univ Dept Math Blacksburg VA 24061 USA Rice Univ Dept Computat & Appl Math Houston TX 77005 USA

Krylov subspace methods have led to reliable and effective tools for resolving large-scale, non-Hermitian eigenvalue problems. Since practical considerations often limit the dimension of the approximating Krylov subspace, modern algorithms attempt to identify and condense significant components from the current subspace, encode them into a polynomial filter, and then restart the Krylov process with a suitably refined starting vector. In effect, polynomial filters dynamically steer low-dimensional Krylov spaces toward a desired invariant subspace through their action on the starting vector. The spectral complexity of nonnormal matrices makes convergence of these methods difficult to analyze, and these effects are further complicated by the polynomial filter process. The principal object of study in this paper is the angle an approximating Krylov subspace forms with a desired invariant subspace. Convergence analysis is posed in a geometric framework that is robust to eigenvalue ill-conditioning, yet remains relatively uncluttered. The bounds described here suggest that the sensitivity of desired eigenvalues exerts little influence on convergence, provided the associated invariant subspace is well-conditioned;ill-conditioning of unwanted eigenvalues plays an essential role. This framework also gives insight into the design of effective polynomial filters. Numerical examples illustrate the subtleties that arise when restartirig non-Hermitian iterations.

关键词： Krylov subspaces Arnoldi algorithm lanczos algorithm eigenvalue computations containment gap pseudospectra

来源：评论

学校读者我要写书评

暂无评论

Conjugate Gradient algorithm in the Four-Dimensional Variational Data Assimilation System in GRAPES

引用

Journal of Meteorological Research 2018年第6期32卷 974-984页

作者： Yongzhu LIU Lin ZHANG Zhihua LIAN National Meteorological Center Beijing 100081

Minimization algorithms are singular components in four-dimensional variational data assimilation(4DVar).In this paper,the convergence and application of the conjugate gradient algorithm(CGA),which is based on the lanczos iterative algorithm and the Hessian matrix derived from tangent linear and adjoint models using a non-hydrostatic framework,are investigated in the 4DVar ***,the influence of the Gram-Schmidt orthogonalization of the lanczos vector on the convergence of the lanczos algorithm is *** results show that the lanczos algorithm without orthogonalization fails to converge after the ninth iteration in the 4DVar minimization,while the orthogonalized lanczos algorithm converges ***,the convergence and computational efficiency of the CGA and quasi-Newton method in batch cycling assimilation experiments are compared on the 4DVar platform of the Global/Regional Assimilation and Prediction System(GRAPES).The CGA is 40%more computationally efficient than the quasi-Newton method,although the equivalent analysis results can be obtained by using either the CGA or the quasi-Newton ***,the CGA based on lanczos iterations is better for solving the optimization problems in the GRAPES 4DVar system.

关键词： numerical weather prediction Global/Regional Assimilation and Prediction System four-dimensional variation conjugate gradient algorithm lanczos algorithm

来源：评论

学校读者我要写书评

暂无评论

Krylov subspace methods for the Dirac equation

引用

COMPUTER PHYSICS COMMUNICATIONS 2015年 188卷 189-197页

作者： Beerwerth, Randolf Bauke, Heiko Max Planck Inst Kernphys D-69117 Heidelberg Germany

The lanczos algorithm is evaluated for solving the time-independent as well as the time-dependent Dirac equation with arbitrary electromagnetic fields. We demonstrate that the lanczos algorithm can yield very precise eigenenergies and allows very precise time propagation of relativistic wave packets. The unboundedness of the Dirac Hamiltonian does not hinder the applicability of the lanczos algorithm. As the lanczos algorithm requires only matrix vector products and inner products, which both can be efficiently parallelized, it is an ideal method for large-scale calculations. The excellent parallelization capabilities are demonstrated by a parallel implementation of the Dirac lanczos propagator utilizing the Message Passing Interface standard. Program summary Program title: Dirac_Laczos Catalogue identifier: AEUY_v1_0 Program summary URL: http://***/summaries/AEUY_v1_*** Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://***/licence/*** No. of lines in distributed program, including test data, etc.: 526428 No. of bytes in distributed program, including test data, etc.: 2 181 729 Distribution format: *** Programming language: C++11. Computer: Multi-core systems or cluster computers. Operating system: Any. Has the code been vectorized or parallelized?: Parallelized using MPI. RAM: Typically 10 megabyte to 1 gigabyte depending on the chosen problem size Classification: 2.7. External routines: Boost [1], LAPACK [2] Nature of problem: Solving the time-dependent Dirac equation in two spatial dimensions Solution method: lanczos propagator Running time: Depending on the problem size and computer hardware typically several minutes to several days References: [1] Boost C++ Libraries, http://*** [2] LAPACK-Linear Algebra PACKage, http://***/lapack/ (C) 2014 Elsevier B.V. All rights reserved.

关键词： Dirac equation Krylov subspace methods lanczos algorithm

来源：评论

学校读者我要写书评

暂无评论

Analysis of projection methods for solving linear systems with multiple right-hand sides

引用

SIAM JOURNAL ON SCIENTIFIC COMPUTING 1997年第6期18卷 1698-1721页

作者： Chan, TF Wan, WL Department of Mathematics Univ. of California at Los Angeles Los Angeles CA 90024 United States

We analyze a class of Krylov projection methods but mainly concentrate on a specific conjugate gradient (CG) implementation by Smith, Peterson, and Mittra [IEEE transactions on Antennas and Propogation, 37 (1989), pp. 1490-1493] to solve the linear system AX = B, where A is symmetric positive definite and B is a multiple of right-hand sides, This method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the CG method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The whole process is repeated with another unsolved system as a seed until all the systems are solved. We observe in practice a superconvergence behavior of the CG process of the seed system when compared with the usual CG process. We also observe that only a small number of restarts is required to solve all the systems if the right-hand sides are close to each other. These two features together make the method particularly effective. In this paper, we give theoretical proof to justify these observations. Furthermore, we combine the advantages of this method and the block CG method and propose a block extension of this single seed method.

关键词： linear systems multiple right-hand sides Krylov space lanczos algorithm conjugate gradient method

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：