检索结果-内蒙古大学图书馆

On stabilization and convergence of clustered Ritz values in the lanczos method

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2005年第3期27卷 891-908页

作者： Wülling, W Univ Bielefeld Fak Math D-33501 Bielefeld Germany

The lanczos algorithm can be considered as an iterative method for finding a few eigenvalues and eigenvectors of large sparse symmetric matrices. In the present paper we solve a conjecture posed by Zdenek Strakos and Anne Greenbaum in [Open Questions in the Convergence Analysis of the lanczos Process for the Real Symmetric Eigenvalue Problem, IMA Research Report, 1992] on the clustering of Ritz values, which occurs in finite precision computations. In particular, we prove that the conjecture is valid in most cases and describe the rare case when it is not. The established upper bounds measuring the quality of Ritz approximations imply also that Ritz values cluster only close to an eigenvalue.

关键词： eigenvalues Ritz values lanczos algorithm tridiagonal matrix

来源：评论

学校读者我要写书评

暂无评论

The stabilization of weights in the lanczos and Conjugate Gradient method

引用

BIT NUMERICAL MATHEMATICS 2005年第2期45卷 395-414页

作者： Wülling, W Univ Bielefeld Fak Math D-33501 Bielefeld Germany

The lanczos and the Conjugate Gradient method both compute implicitly a sequence of Gauss quadrature approximations to a certain Riemann-Stieltjes integral. In finite precision computations the corresponding weight function will be slightly perturbed. The purpose of this paper is to solve a conjecture posed by Anne Greenbaum and Zdenek Strakos on the stabilization of weights for the Gauss quadrature approximations, i.e. in particular we prove that for a tight well separated cluster of Ritz values (nodes) an upper bound for the change in the sum of the corresponding weights can be developed that depends mainly on the ratio of the cluster diameter and the gap in the spectrum.

关键词： lanczos algorithm Conjugate Gradient method tridiagonal matrix Gauss-quadrature stabilization of weights

来源：评论

学校读者我要写书评

暂无评论

An orthogonal similarity reduction of a matrix into semiseparable form

引用

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2005年第1期27卷 176-197页

作者： Van Barel, M Vandebril, R Mastronardi, N Katholieke Univ Leuven Dept Comp Sci B-3001 Louvain Heverlee Belgium CNR Sez Bari Ist Applicaz Calcolo M Picone I-70126 Bari Italy

An algorithm to reduce a symmetric matrix to a similar semiseparable one of semiseparability rank 1, using orthogonal similarity transformations, is proposed in this paper. It is shown that, while running to completion, the proposed algorithm gives information on the spectrum of the similar initial matrix. In fact, the proposed algorithm shares the same properties of the lanczos method and the Householder reduction to tridiagonal form. Furthermore, at each iteration, the proposed algorithm performs a step of the QR method without shift to a principal submatrix to retrieve the semiseparable structure. The latter step can be considered a kind of subspace-like iteration method, where the size of the subspace increases by one dimension at each step of the algorithm. Hence, when during the execution of the algorithm the Ritz values approximate the dominant eigenvalues closely enough, diagonal blocks will appear in the semiseparable part where the norm of the corresponding subdiagonal blocks goes to zero in the subsequent iteration steps, depending on the corresponding gap between the eigenvalues. A numerical experiment is included, illustrating the properties of the new algorithm.

关键词： similarity transformation semiseparable matrix lanczos algorithm Ritz values

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

On the construction of a reduced rank square-root Kalman filter for efficient uncertainty propagation

引用

FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE 2005年第7期21卷 1047-1055页

作者： Treebushny, D Madsen, H NAS Ukraine Inst Math Machines & Syst Problems Kiev Ukraine Danish Hydraul Inst Water & Environm DK-2970 Horsholm Denmark

The Kalman filter is a sequential estimation procedure that combines a stochastic dynamical model with observations in order to update the model state and the associated uncertainty. In the situation where no measurements are available the filter works as an uncertainty propagator. The most computationally demanding part of the Kalman filter is to propagate the covariance through the dynamical system, which may be completely infeasible in high-dimensional models. The reduced rank square-root (RRSQRT) filter is a special formulation of the Kalman filter for large-scale applications. In this formulation, the covariance matrix of the model state is expressed in a limited number of modes M. In the classical implementation of the RRSQRT filter the computational costs of the truncation step grow very fast with the number of modes (> M-3). In this work, a new approach based on the Lanzcos algorithm is formulated. It provides a more cost-efficient scheme and includes a precision coefficient that can be tuned for specific applications depending on the trade-off between precision and computational load. (c) 2004 Elsevier B.V. All rights reserved.

关键词： Kalman filter reduced rank square-root RRSQRT lanczos algorithm

来源：评论

学校读者我要写书评

暂无评论

On the construction of a reduced rank square-root Kalman filter for efficient uncertainty propagation

On the construction of a reduced rank square-root Kalman fil...

引用

International Conference on Computational Sciences

作者： Treebushny, D Madsen, H NAS Ukraine Inst Math Machines & Syst Problems Kiev Ukraine Danish Hydraul Inst Water & Environm DK-2970 Horsholm Denmark

关键词： Kalman filter reduced rank square-root RRSQRT lanczos algorithm

来源：评论

学校读者我要写书评

暂无评论

A Krylov subspace method for information retrieval

引用

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2004年第2期26卷 566-582页

作者： Blom, K Ruhe, A Chalmers Dept Comp Sci SE-41296 Gothenburg Sweden Univ Gothenburg SE-41296 Gothenburg Sweden Royal Inst Technol Dept Numer Anal & Comp Sci NADA SE-10044 Stockholm Sweden

A new algorithm for information retrieval is described. It is a vector space method with automatic query expansion. The original user query is projected onto a Krylov subspace generated by the query and the term-document matrix. Each dimension of the Krylov space is generated by a simple vector space search, using first the user query and then new queries generated by the algorithm and orthogonal to the previous query vectors. The new algorithm is closely related to latent semantic indexing (LSI), but it is a local algorithm that works on a new subspace of very low dimension for each query. This makes it faster and more flexible than LSI. No preliminary computation of the singular value decomposition (SVD) is needed, and changes in the data base cause no complication. Numerical tests on both small (Cranfield) and larger (Financial Times data from the TREC collection) data sets are reported. The new algorithm gives better precision at given recall levels than simple vector space and LSI in those cases that have been compared.

关键词： information retrieval vector space model query expansion latent semantic indexing singular value decomposition lanczos algorithm Krylov subspace

来源：评论

学校读者我要写书评

暂无评论

Methods for calculating vibrational energy levels

引用

CANADIAN JOURNAL OF CHEMISTRY 2004年第6期82卷 900-914页

作者： Carrington, T Univ Montreal Dept Chim Montreal PQ H3C 3J7 Canada

This article reviews new methods for computing vibrational energy levels of small polyatomic molecules. The principal impediment to the calculation of energy levels is the size of the required basis set. If one uses a product basis the Hamiltonian matrix for a four-atom molecule is too large to store in core memory. We discuss iterative methods that enable one to use a product basis to compute energy levels (and spectra) without storing a Hamiltonian matrix. Despite the advantages of iterative methods it is not possible, using product basis functions, to calculate vibrational spectra of molecules with more than four atoms. A very recent method combining contracted basis functions and the lanczos algorithm with which vibrational energy levels of methane have been computed is described. New ideas, based on exploiting preconditioning, for reducing the number of matrix-vector products required to converge energy levels of interest are also summarized.

关键词： vibrational energy levels kinetic energy operators lanczos algorithm contracted basis functions preconditioning

来源：评论

学校读者我要写书评

暂无评论

External selective orthogonalization for the lanczos algorithm in distributed memory environments

引用

PARALLEL COMPUTING 2001年第7期27卷 913-923页

作者： Cooper, A Szularz, M Weston, J Univ Ulster Sch Informat & Software Engn Coleraine BT52 1SA Londonderry North Ireland

The k-step explicit restart lanczos algorithm, LExpRes, for the computation of a few of the extreme eigenpairs of large, usually sparse, symmetric matrices, computes one eigenpair at a time using a deflation technique in which each lanczos vector generated is orthogonalized against all previously converged eigenvectors. The computation of the inner products associated with this external orthogonalization often creates a bottleneck in parallel distributed memory environments. In this paper methods are proposed which significantly reduce this computational overhead in LExpRes, thereby effectively improving its efficiency. The performances of these methods on the Cray-T3D and the Cray-T3E are assessed and critically compared with that of the original algorithm. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： lanczos algorithm restarting deflation reorthogonalization MPP

来源：评论

学校读者我要写书评

暂无评论

Theoretical studies of (A)over-tilde¹A" → (X)over-tilde¹A′ resonance emission spectra of HCN/DCN using single lanczos propagation method

引用

JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2003年第4期2卷 639-648页

作者： Xu, DG Guo, H Xie, DQ Univ New Mexico Dept Chem Albuquerque NM 87131 USA Nanjing Univ Dept Chem Nanjing 210008 Jiangsu Peoples R China Nanjing Univ Inst Theoret & Computat Chem Nanjing 210008 Jiangsu Peoples R China Sichuan Univ Dept Chem Chengdu Sichuan Peoples R China

Using an efficient single lanczos propagation method, we report the (A) over tilde (1)A", (X) over tilde (1)A' resonance emission spectra of HCN and DCN from a number of low-lying vibrational levels of the A-state manifold. Our calculations represent the first such undertaking in which a high-quality ab initio based potential energy surface of the excited ((a) over tilde (1)A") state and a (A) over tilde (1)A"-(X) over tilde (1)A' transition dipole surface were used. The results show a significant improvement over previous theoretical work in reproducing experimental stimulated emission pumping spectra of HCN. The improved theory-experiment agreement is attributed to the accurate (A) over tilde -state potential energy surface, while the impact of the transition dipole function was found to be relatively minor.

关键词： lanczos algorithm emission spectrum

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：