位置：成果数据库 > 期刊 > 期刊详情页
The RCH method for computing minimal polynomials of polynomial matrices
  • ISSN号：1009-6124
  • 期刊名称：Journal of Systems Science and Complexity
  • 时间：2015.2.25
  • 页码：190-209-
  • 分类：O151.21[理学—数学;理学—基础数学] TN918.1[电子电信—通信与信息系统;电子电信—信息与通信工程]
  • 作者机构：[1]School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China., [2]School of Science, Dalian University of Technology, Panjin 124221, China.
  • 相关基金：This research was supported by the National Natural Science Foundation of China under Grant No. 11171051, the Major Research plan of the National Natural Science Foundation of China under Grant No. 91230103 and the Fundamental Research Funds for the Central Universities under Grant No. DUT14RC（3）023.
  • 相关项目：非凸与非光滑优化的高效率全局收敛算法
作者： Zhang, Jintao|Zhang, Jintao|Xu, Yanyan|Xu, Yanyan|
关键词： 多项式矩阵, 极小多项式, RCH, 计算, 最小多项式, 模块化技术, 复杂性分析, 随机, Characteristic polynomial, minimal polynomial, polynomial matrix.
中文摘要：

在这份报纸，一条使随机化的 Cayley-Hamilton 定理基于方法(由 RCH 方法缩短了) 为计算，一个多项式矩阵的最小的多项式被介绍。它到条款决定系数多项式条款从对更高的度更低。由使用随机的向量并且随机变，它不与概率一在输入矩阵和工作上要求条件。在给定的多项式矩阵的条目的系数都是整数并且算法在准确计算被执行的情况中，由使用模块化的技术， RCH 方法的一个 parallelized 版本也被给。有在两理论复杂性分析和计算测试的另外的算法的比较被给显示出它的有效性。

英文摘要：

In this paper, a randomized Cayley-Hamilton theorem based method （abbreviated by RCH method） for computing the minimal polynomial of a polynomial matrix is presented. It determines the coefficient polynomials term by term from lower to higher degree. By using a random vector and randomly shifting, it requires no condition on the input matrix and works with probability one. In the case that coefficients of entries of the given polynomial matrix are all integers and that the algorithm is performed in exact computation, by using the modular technique, a parallelized version of the RCH method is also given. Comparisons with other algorithms in both theoretical complexity analysis and computational tests are given to show its effectiveness.

同期刊论文项目
非凸与非光滑优化的高效率全局收敛算法
期刊论文 140 会议论文 4
高维数据的低维非线性逼近中的非凸优化模型的有效解法和软件
期刊论文 163 会议论文 11
同项目期刊论文
EFFICIENT HOMOTOPY SOLUTION AND A CONVEX COMBINATION OF ROF AND LLT MODELS FOR IMAGE RESTORATION
A 3D multi-grid algorithm for the Chan-Vese model of variational image segmentation
Homotopy method for a mean curvature-based denoising model
HOMOTOPY CURVE TRACKING FOR TOTAL VARIATION IMAGE RESTORATION
A constraint shifting homotopy method for convex multi-objective programming
A SMOOTHING HOMOTOPY METHOD BASED ON ROBINSON'S NORMAL EQUATION FOR MIXED COMPLEMENTARITY PROBL
A Spline Smoothing Newton Method for Semi-Infinite Minimax Problems
A modified homotopy method for solving nonconvex fixed points problems
Eigenfunction expansion method for multiple solutions of semilinear elliptic equations with polynomi
AN ITERATIVE LAGRANGE MULTIPLIER METHOD FOR CONSTRAINED TOTAL-VARIATION-BASED IMAGE DENOISING
Distributionally Robust Return-Risk Optimization Models and Their Applications
A Spline Smoothing Newton Method for L∞ Distance Regression with Bound Constraints
IMAGE DENOISING USING LLT MODEL AND ITERATED TOTAL VARIATION REFINEMENT
The Flattened Aggregate Constraint Homotopy Method for Nonlinear Programming Problems with Many Nonl
A smoothing homotopy method for variational inequality problems on polyhedral convex sets
A local information based variational model for selective image segmentation
A homotopy method for nonlinear semidefinite programming
A homotopy method based on penalty function for nonlinear semidefinite programming
A symmetric homotopy and hybrid polynomial system solving method for mixed trigonometric polynomial
非线性LTS估计的截断凝聚光滑化方法
Generalized Local-to-global Shape Feature Detection based on Graph Wavelets.
Adomian decomposition method is a special case of Lyapunov's artificial small parameter method
A spline smoothing Newton method for finite minimax problems
Batch gradient method with smoothing L1 / 2 regularization for training of feedforward neural networ
Direct GBQ Algorithm for Solving Mixed Trigonometric Polynomial Systems
A constraint shifting spline smoothing homotopy method for general nonlinear programming,
Fast L0-Regularized Kernel Estimation for Robust Motion Deblurring
Globally convergent homotopy method for designing piecewise linear deterministic contractual functio
An open problem on the optimality of an asymptotic solution to Duffing's nonlinear oscillation
Diffuse visual attention for saliency detection
Primary correspondences between intrinsically symmetrical shapes
Polynomial Homotopy Method for the Sparse Interpolation Problem Part I:Equally Spaced Sampling
Object level saliency by submodular optimization
Solving path planning of UAV based on modified multi-population differential evolution algorithm
Fabric defect inspection using prior knowledge guided least squares regression
Quadratic inverse eigenvalue problem for damped gyroscopic systems
Laplace transform for the solution of higher order deformation equations arising in the homotopy ana
The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems
Normal-controlled coordinates based feature-preserving mesh editing
A constraint shifting homotopy method for general non-linear programming
A constraint shifting spline smoothing homotopy method for general nonlinear programming
CVaR-constrained stochastic programming reformulation for stochastic nonlinear complementarity probl
Structure-Constrained Low-Rank Representation
Double parallel feedforward neural network based on extreme learning machine with L1/2 regularizer
A pruning algorithm with L_(1/2) regularizer for extreme learning machine
A modified gradient learning algorithm with smoothing L1/2 regularization for Takagi-Sugeno fuzzy mo
Convergence of online gradient method for feedforward neural networks with smoothing L1/2 regulariza
A relaxed fixed point method for a mean curvature-based denoising model
Particle Swarm Optimization Based on Local Attractors of Ordinary Differential Equation System
Proof of a conjecture on a discretized elliptic equation with cubic nonlinearity
Bayesian low-rank and sparse nonlinearrepresentation for manifold clustering
Geometry image with higher compressibility
Robust Visual Tracking via DescriminativeSequential Ranking
A homotopy method for nonlinear second-order cone programming
A note on the relation between the newton homotopy method and the damped Newton method
Truncated aggregate homotopy method for nonconvex nonlinear programming
Efficiently Counting Affine Roots of Mixed Trigonometric Polynomial Systems
Augmented Lagrangian Alternating Direction Method for Tensor RPCA
CDG方程和耦合KdV-MKdV方程的微分不变量
l1优化在网格去噪中的应用
期刊信息
  • 《系统科学与复杂性学报：英文版》
  • 主管单位:中国科学院
  • 主办单位:中国科学院系统科学研究所
  • 主编：
  • 地址：北京东黄城根北街16号
  • 邮编：100080
  • 邮箱：
  • 电话：010-62541831 62541834
  • 国际标准刊号：ISSN：1009-6124
  • 国内统一刊号：ISSN：11-4543/O1
  • 邮发代号:82-545
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,荷兰文摘与引文数据库,美国工程索引,美国科学引文索引（扩展库）,英国科学文摘数据库
  • 被引量:125