Hybrid Iterative Refined Method for Computing a Few Extreme Eigenpairs of a Symmetric Matrix

2021 ◽  
pp. S200-S224
Author(s):  
James Baglama ◽  
Tom Bella ◽  
Jennifer Picucci
Keyword(s):  
Symmetric Matrix ◽  
Refined Method

Fast Bilinear Algorithms for Symmetric Tensor Contractions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Edgar Solomonik ◽  
James Demmel
Keyword(s):  
Symmetric Matrix ◽  
Matrix Multiplication ◽  
Computational Cost ◽  
Symmetric Tensor ◽  
Partial Sums ◽  
Symmetric Tensors ◽  
Outer Product ◽  
Bilinear Complexity ◽  
Special Cases ◽  
Tensor Contractions

AbstractIn matrix-vector multiplication, matrix symmetry does not permit a straightforward reduction in computational cost. More generally, in contractions of symmetric tensors, the symmetries are not preserved in the usual algebraic form of contraction algorithms. We introduce an algorithm that reduces the bilinear complexity (number of computed elementwise products) for most types of symmetric tensor contractions. In particular, it lowers the bilinear complexity of symmetrized contractions of symmetric tensors of order {s+v} and {v+t} by a factor of {\frac{(s+t+v)!}{s!t!v!}} to leading order. The algorithm computes a symmetric tensor of bilinear products, then subtracts unwanted parts of its partial sums. Special cases of this algorithm provide improvements to the bilinear complexity of the multiplication of a symmetric matrix and a vector, the symmetrized vector outer product, and the symmetrized product of symmetric matrices. While the algorithm requires more additions for each elementwise product, the total number of operations is in some cases less than classical algorithms, for tensors of any size. We provide a round-off error analysis of the algorithm and demonstrate that the error is not too large in practice. Finally, we provide an optimized implementation for one variant of the symmetry-preserving algorithm, which achieves speedups of up to 4.58\times for a particular tensor contraction, relative to a classical approach that casts the problem as a matrix-matrix multiplication.

scholarly journals The location of classified edges due to the change in the geometric multiplicity of an eigenvalue in a tree

2019 ◽  
Vol 7 (1) ◽  
pp. 257-262
Author(s):  
Kenji Toyonaga
Keyword(s):  
Symmetric Matrix ◽  
Symmetric Matrices ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Multiplicity ◽  
Necessary And Sufficient ◽  
Multiplicity Of An Eigenvalue

Abstract Given a combinatorially symmetric matrix A whose graph is a tree T and its eigenvalues, edges in T can be classified in four categories, based upon the change in geometric multiplicity of a particular eigenvalue, when the edge is removed. We investigate a necessary and sufficient condition for each classification of edges. We have similar results as the case for real symmetric matrices whose graph is a tree. We show that a g-2-Parter edge, a g-Parter edge and a g-downer edge are located separately from each other in a tree, and there is a g-neutral edge between them. Furthermore, we show that the distance between a g-downer edge and a g-2-Parter edge or a g-Parter edge is at least 2 in a tree. Lastly we give a combinatorially symmetric matrix whose graph contains all types of edges.

Refined Optimization Analysis of 2G/3G Mode Switching

2013 ◽  
Vol 443 ◽  
pp. 349-353
Author(s):  
Yu Zhang ◽  
Chun Yang Wang
Keyword(s):  
Basic Principle ◽  
Implementation Process ◽  
Typical Case ◽  
Mode Switching ◽  
Continuous Development ◽  
Optimization Analysis ◽  
Refined Method ◽  
High Efficient ◽  
Specific Implementation

With the continuous development of the 3rd generation telecommunication, the requirement of fluent switching is taken more consideration. The paper presents the relevant parameters and the implication of 2G/3G mode switching in CS domain. Proposes the optimization analysis of the basic principle of 2G/3G mode switching in CS domain, suggests a method using neighboring CIO to refine the origin switching methods, with the analysis of typical case by using the specific implementation process of neighboring CIO, the refined method proved to be of actual value and high efficient

New zeroing neural dynamics models for diagonalization of symmetric matrix stream

2019 ◽  
Vol 85 (3) ◽  
pp. 849-866 ◽  
Author(s):  
Yunong Zhang ◽  
Huanchang Huang ◽  
Min Yang ◽  
Yihong Ling ◽  
Jian Li ◽  
...  
Keyword(s):  
Symmetric Matrix ◽  
Neural Dynamics ◽  
Dynamics Models

scholarly journals Overlapping Community Discovery Method Based on Two Expansions of Seeds

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 18
Author(s):  
Yan Li ◽  
Jing He ◽  
Youxi Wu ◽  
Rongjie Lv
Keyword(s):  
Symmetric Matrix ◽  
Fitness Function ◽  
Local Maximum ◽  
Community Discovery ◽  
Network Nodes ◽  
Overlapping Community ◽  
The Common ◽  
New Research ◽  
Discovery Method ◽  
Discovery Algorithms

The real world can be characterized as a complex network sto in symmetric matrix. Community discovery (or community detection) can effectively reveal the common features of network groups. The communities are overlapping since, in fact, one thing often belongs to multiple categories. Hence, overlapping community discovery has become a new research hotspot. Since the results of the existing community discovery algorithms are not robust enough, this paper proposes an effective algorithm, named Two Expansions of Seeds (TES). TES adopts the topological feature of network nodes to find the local maximum nodes as the seeds which are based on the gravitational degree, which makes the community discovery robust. Then, the seeds are expanded by the greedy strategy based on the fitness function, and the community cleaning strategy is employed to avoid the nodes with negative fitness so as to improve the accuracy of community discovery. After that, the gravitational degree is used to expand the communities for the second time. Thus, all nodes in the network belong to at least one community. Finally, we calculate the distance between the communities and merge similar communities to obtain a less- undant community structure. Experimental results demonstrate that our algorithm outperforms other state-of-the-art algorithms.

New Type of Two Degree of Freedom Motor Three-Dimensional Tooth Layer Field Application and Solution

2013 ◽  
Vol 391 ◽  
pp. 232-236
Author(s):  
Wen Huan Yang ◽  
Hai Xu Chen ◽  
Shuang Xie ◽  
Chun Ren Fang
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Field Application ◽  
Degree Of Freedom ◽  
Refined Method ◽  
New Type ◽  
Type Motor ◽  
Quasi Newton ◽  
Two Degree Of Freedom ◽  
Non Linear Equations

A new Multi-degree of freedom motor and its establishing of teeth layer parameters have been introduced in the paper, also including application method of database, namely using Quasi-Newton methods to solve the non-linear equations of the new motors magnetic circuit net, formed a refined method for designing and analyzing of motor. The establishment of 3d tooth layer parameters database, is provided for the calculation in the design of the new type motor conveniently.

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