检索结果-内蒙古大学图书馆

THE ADVANTAGES OF INVERTED OPERATORS IN RAYLEIGH-RITZ APPROXIMATIONS

SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING 1982年第1期3卷 68-75页

作者： SCOTT, DS

Generalized eigenvalue problems are often solved by a combination of inverse iteration and the Rayleigh–Ritz procedure. In this paper we show that significant advantages can be obtained in this context by applying the Rayleigh–Ritz procedure to an inverted operator, either explicitly while using subspace iteration or implicitly by applying the lanczos algorithm to the inverted operator. Since the lanczos algorithm is much more powerful than subspace iteration it should be used whenever possible.

关键词： eigenvalues eigenvectors symmetric matrices Rayleigh–Ritz procedure lanczos algorithm

来源：评论

学校读者我要写书评

暂无评论

A parallel implementation of a generalized lanczos procedure for structural dynamic analysis

引用

INTERNATIONAL JOURNAL OF HIGH SPEED COMPUTING 1996年第2期8卷 171-204页

作者： Mackay, DR Law, KH STANFORD UNIV DEPT CIVIL ENGN STANFORD CA 94305 USA

The lanczos method has rapidly become the preferred method of solution for the generalized eigenvalue problems. The recent emergence of parallel computers has aroused much interest in the practical implementation of the lanczos algorithm on these high performance computers. This paper describes an implementation of a generalized lanczos algorithm on a distributed memory parallel computer, with specific application to structural dynamic analysis. One major cost in the parallel implementation of the generalized lanczos procedure is the factorization of the (shifted) stiffness matrix and the forward and backward solution of triangular systems. In this paper, we review a parallel sparse matrix factorization scheme and propose a strategy for inverting the principal block submatrix factors to facilitate the forward and backward solution of triangular systems on distributed memory parallel computers. We also discuss the different strategies in the implementation of mass-matrix-vector multiplication and how they are used in the implementation of the lanczos procedure. The lanczos procedure implemented includes partial and external selective reorthogonalizations. Spectral shifts are introduced when memory space is not sufficient for storing the lanczos vectors. The tradeoffs between spectral shifts and lanczos iterations are discussed. Numerical results on Intel's parallel computers, the iPSC/860 hypercube and the Paragon machines will be presented to illustrate the effectiveness and scalability of the parallel generalized lanczos procedure.

关键词： eigenvalues lanczos algorithm sparse matrices parallel matrix computation structural dynamics

来源：评论

学校读者我要写书评

暂无评论

FPGA-Based Hardware Accelerator for Matrix Inversion

引用

SN Computer Science 2023年第2期4卷 147页

作者： Kokkiligadda, Venkata Siva Kumar Naikoti, Vijitha Patkotwar, Gaurao Sunil Sabat, Samrat L. Peesapati, Rangababu Centre for Advanced Studies in Electronics Science and Technology University of Hyderabad Telangana Hyderabad 500046 India Department of Electronics and Communications Engineering NIT Meghalaya Meghalaya Shillong 793001 India

Matrix inversion is a computationally expensive operation in many scientific applications. Performing matrix inversion of rank deficient large order matrices is still a challenge due to its computational overhead. This paper presents the hardware implementation of matrix inversion with (i) singular value decomposition (SVD) based on lanczos and implicit triQR algorithms, (ii) QR method that uses modified Gram–Schmidt (MGS) technique and (iii) inbuilt linear algebra package QR inverse using Xilinx Vivado high level synthesis platform. All the three algorithms are implemented on Pynq-Z1 Field Programmable Gate Array (FPGA) using System on Chip (SoC) approach. The resource utilization along with accuracy, hardware execution time with and without loop optimization are reported for the aforementioned matrix inversion techniques of different matrix sizes. We achieved the hardware acceleration factor with loop optimization as 111x and 104x, respectively, for the matrix inversion of the MGS algorithm and SVD based on lanczos algorithm with respect to the software implementation execution time on Pynq-Z1 FPGA for the matrix size 90 × 90. © 2022, The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.

关键词： Implicit triQR lanczos algorithm Matrix inversion Modified Gram–Schmidt QR decomposition SVD algorithm

来源：评论

学校读者我要写书评

暂无评论

EIT Complex Admitance Reconstruction through Intervalar Evaluation 12

EIT Complex Admitance Reconstruction through Intervalar Eval...

引用

12th IFAC Symposium on Biological and Medical Systems (BMS)

作者： Martins, Thiago C. Tsuzuki, Marcos S. G. Escola Politecn Univ Sao Paulo Computat Geometry Lab Sao Paulo Brazil

Electrical Impedance Tomography (EIT) stands out as a widely utilized imaging method. It becomes crucial to recover the intricate admittance in EIT for various purposes, particularly when the interest extends beyond mere visualization of fixed conductivity (or resistivity) patterns within a region. This study addresses a complex EIT inverse problem, which involves reconstructing the complex distribution of admittance based on surface potential measurements and corresponding injected currents. A Bayesian approach leads to Maximum a Posteriori Reconstructions using non-convex optimization. This paper adapts non-convex optimization approaches to EIT to handle the non-Hermitian FEM models that arise from complex admittance. Finally, a synthetic phantom experiment was conducted, demonstrating the successful reconstruction of the overall shape of the admittance distribution. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)

关键词： Electrical Impedance Tomography Inverse Problems Simulated Annealing lanczos algorithm Preconditioning

来源：评论

学校读者我要写书评

暂无评论

A Low Complexity Greedy algorithm for Dynamic Subarrays in mmWave MIMO Systems 90

A Low Complexity Greedy Algorithm for Dynamic Subarrays in m...

引用

90th IEEE Vehicular Technology Conference (IEEE VTC-Fall)

作者： Xu, Ke Zheng, Fu-Chun Cao, Pan Xu, Hongguang Zhu, Xu Harbin Inst Technol Shenzhen Sch Elect & Informat Engn Shenzhen Peoples R China Univ Hertfordshire Sch Engn & Technol Hatfield AL10 9AB Herts England Pengcheng Lab Shenzhen Peoples R China

ISBN: (纸本)9781728112206

For a mmWave multiple input multiple output (MIMO) system, the hybrid precoding scheme is of great interest due to its lower power consumption and hardware cost, where a smaller number of RF chains are used to feed a larger scale of antenna array. In this paper we consider a flexible architecture where RF chains and antennae can be dynamically connected, and propose a greedy algorithm to achieve dynamic subarray configuration. The greedy algorithm can select the best subarrays from all the possible candidates in each search process, while the lanczos algorithm is applied to further reduce the computation complexity. Simulation results demonstrate the superior performance of the proposed algorithm to existing works yet with a lower complexity.

关键词： Massive MIMO mmWave communications hybrid precoding dynamic subarrays lanczos algorithm

来源：评论

学校读者我要写书评

暂无评论

A Distance-Based Spectral Clustering Approach with Applications to Network Community Detection 23

A Distance-Based Spectral Clustering Approach with Applicati...

引用

23rd ISPE Inc. International Conference on Transdisciplinary Engineering

作者： Shen, Gang Ye, Dongmei Huazhong Univ Sci & Technol Sch Software Engn Wuhan 430074 Peoples R China

ISBN: (纸本)9781614997030;9781614997023

Object clustering is a fundamental task in many data analysis and pattern understanding applications by providing insights into detecting the underlying structures of a large collection of samples. In this paper, we present our work on a novel spectral clustering algorithm that partitions a collection of objects using the spectrum of adistance matrix. If the nodes in a metric space can be associated with a well defined distance, the distance matrix is almost negative definite, implying that the eigenvector for the smallest eigenvalues of this matrix can be used as an approximation of the solution to a quadratic form partition problem. It is proved that this smallest eigenvalue is equivalent to the second largest singular value. Therefore lanczos iterative algorithm can be applied to findingthe eigenvalues efficiently. We adapted this algorithm to the distributed network community detection problem using a decentralized multi-agent framework, and tested the effectiveness of the proposed approach with simulations.

关键词： Spectral clustering network community detection multi-agent systems almost negative definite matrices lanczos algorithm

来源：评论

学校读者我要写书评

暂无评论

The triangular decomposition of hank el matrices

引用

Mathematics of Computation 1971年第115期25卷 599-602页

作者： Phillips, James L. Computer Science Department Washington State University Pullman WA 99163 United States

An algorithm for determining the triangular decomposition H = R*DR of a Hankel matrix H using 0(/i2) operations is derived. The derivation is based on the lanczos algorithm and the relation between orthogonalization of vectors and the triangular decomposition of moment matrices. The algorithm can be used to compute the three-term recurrence relation for orthogonal polynomials from a moment matrix. © 1971 American Mathematical Society.

关键词： Hankel matrix lanczos algorithm Moment matrix Orthogonal polynomials Orthogonalization Three-term recurrence relations Triangular decomposition of matrices

来源：评论

学校读者我要写书评

暂无评论

Gauss Quadrature Rule Based on Parameter Estimation

Gauss Quadrature Rule Based on Parameter Estimation

引用

7th International Symposium on Instrumentation and Control Technology

作者： Xie Kai Yang Shulin Beijing Inst Graph Commun Coll Informat & Mech Engn Beijing 102600 Peoples R China

ISBN: (纸本)9780819473639

In this paper, we consider the estimation of the unknown parameter for the problem of reconstructing a high resolution image from multiple under-sampled, shifted, degraded frames. L-curve criterion is used to estimate regularization parameters. However, the computational of the L-curve is quiet costly for large-size problems. The paper proposes an efficient approximate technique based on Gauss quadrature rule. The technique translates some matrix computation into Gauss quadrature with singular decomposition. It can reduce the computational complexity of the L-curve.

关键词： Gauss quadrature lanczos algorithm L-curve

来源：评论

学校读者我要写书评

暂无评论

SIMULATION OF CONSTRAINED FERMIONS N LOW-DIMENSIONAL SYSTEMS

SIMULATION OF CONSTRAINED FERMIONS N LOW-DIMENSIONAL SYSTEMS

引用

作者： Matthias TROYER Swiss Federal Institute of Technology in Zurich

学位级别：博士

Several numerical methods have been improved and eciently implemented to an- swer some important questions about constrained fermion systems. We have de- veloped an improved version of the quantum transfer matrix algorithm to study quasi one-dimensional systems such as chains or ladders. The extreme eigenval- ues and eigenvectors of the quantum transfer matrix are calculated by the recently developed look-ahead lanczos algorithm. The phase diagram of the one-dimensional Kondo lattice model has been in- vestigated using the quantum Monte Carlo world line algorithm and quantum transfer matrix techniques. In the strong coupling region ferromagnetic ordering is found even at large band llings. In the weak coupling region the system shows a Ruderman-Kittel-Kasuya-Yoshida (RKKY) like behaviour. The one-dimensional t-J model with additional density-density repulsive inter- actions has been studied by exact diagonalisation and quantum Monte Carlo meth- ods. A short-range repulsion pushes phase separation to larger values of J/t, and leads to a widened precursor region in which a spin gap and strengthened super- conducting correlations appear. The correlation exponents and the phase diagram are calculated. The new quantum transfer matrix method has been applied to the antiferro- magnetic Heisenberg S = 1/2 ladder (two coupled chains). The temperature de- pendence of the magnetic susceptibility, specic heat, correlation length and nuclear spin relaxation rate 1/T1 are calculated. The results are compared to experiments on ladder-type compounds. Exact diagonalisation studies for a doped t-J ladder show hole pairing in the ground state. The excitation spectrum separates into a limited number of quasi- particles which carry charge +|e| and spin 1 and a triplet mode. At half-lling the 2 former vanish but the latter evolves continuously into the triplet band of the spin liquid. At low doping the quasiparticles form a dilute Fermi gas with a strong at- traction but simultaneously t

关键词： Quantum transfer matrix lanczos algorithm eigenvectors Low-Dimensional numerical methods Kondo lattice Extreme Eigenvalues CONSTRAINED FERMIONS look-ahead

来源：评论

学校读者我要写书评

暂无评论

Dimensionality Reduction of the Complete Bipartite Graph with K Edges Removed for Quantum Walks

Dimensionality Reduction of the Complete Bipartite Graph wit...

引用

IEEE Nanotechnology Symposium (ANTS)

作者： Koscinski, Viktoria Chiang, Chen-Fu SUNY Polytech Inst Dept Comp Sci Utica NY 13502 USA

ISBN: (纸本)9781538677551

Systematic dimensionality reduction allows for the optimization of quantum search and transport problems on particular graphs. In the past, the lanczos algorithm has been used to perform systematic dimensionality reduction on matrices of graphs including the Complete Graph (CG), the CG with symmetry broken, and Complete Multipartite Graphs (CMPGs), including the Complete Bipartite Graph (CBG). We focus on expanding the scope of these reductions to the CBG with symmetry broken in order to allow the optimization of Quantum Walks on this type of graph. We show that similarly to the CG, the lanczos algorithm can be expanded to the CBG with broken symmetry, which has k random edges removed with the constraints that no more than one edge per node is removed and that no edges that connect to the solution node are removed. Unlike the CG with broken edges, which, after reduction, has 3 types of nodes and a resulting 3x3 matrix, the CBG with broken edges reduces to a graph with 5 types of nodes, resulting in a reduction from an NxN matrix to a 5x5 matrix. From these results, it may be further explored whether or not the more general CMPG reduction may also be expanded by breaking the graph's symmetry, and if so, how the dimensions of the reduced matrices will be affected as the number of partitions grows.

关键词： Quantum Computing Dimensionality Reduction Quantum Walks Complete Bipartite Graph lanczos algorithm Graph Reduction

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：