电脑知识与技术
電腦知識與技術
전뇌지식여기술
Computer Knowledge and Technology
2015年
18期
179-182
,共4页
非负矩阵%谱半径%非负矩阵分解算法%奇异值分解%谱半径计算
非負矩陣%譜半徑%非負矩陣分解算法%奇異值分解%譜半徑計算
비부구진%보반경%비부구진분해산법%기이치분해%보반경계산
non negative matrix%spectral radius%non negative matrix factorization algorithm%singular value decomposition%spec?tral radius calculation
在非负矩阵谱半径的估计、计算的诸多方法中,直接计算方法较少且多采用幂法或对角相似变换而非矩阵分解.由于矩阵分解是矩阵计算中算法设计的主要技巧,且非负矩阵分解有独到的直观解释,为此提出基于该分解计算非负矩阵谱半径的方法:构造了收敛矩阵序列,证明了该序列的谱半径收敛于原矩阵的谱半径;结合矩阵的奇异值分解给出了谱半径计算值的上界.数据实验表明:对相同的非负矩阵,算法迭代次数少而直接给出谱半径的计算值,与估计谱半径上下界的方法相比,前者更精确;对20阶至1500阶的随机矩阵乃至典型的病态矩阵Hilbert矩阵,也以较少的迭代次数得到精确结果.为谱半径的直接计算提供了有效的新方法.
在非負矩陣譜半徑的估計、計算的諸多方法中,直接計算方法較少且多採用冪法或對角相似變換而非矩陣分解.由于矩陣分解是矩陣計算中算法設計的主要技巧,且非負矩陣分解有獨到的直觀解釋,為此提齣基于該分解計算非負矩陣譜半徑的方法:構造瞭收斂矩陣序列,證明瞭該序列的譜半徑收斂于原矩陣的譜半徑;結閤矩陣的奇異值分解給齣瞭譜半徑計算值的上界.數據實驗錶明:對相同的非負矩陣,算法迭代次數少而直接給齣譜半徑的計算值,與估計譜半徑上下界的方法相比,前者更精確;對20階至1500階的隨機矩陣迺至典型的病態矩陣Hilbert矩陣,也以較少的迭代次數得到精確結果.為譜半徑的直接計算提供瞭有效的新方法.
재비부구진보반경적고계、계산적제다방법중,직접계산방법교소차다채용멱법혹대각상사변환이비구진분해.유우구진분해시구진계산중산법설계적주요기교,차비부구진분해유독도적직관해석,위차제출기우해분해계산비부구진보반경적방법:구조료수렴구진서렬,증명료해서렬적보반경수렴우원구진적보반경;결합구진적기이치분해급출료보반경계산치적상계.수거실험표명:대상동적비부구진,산법질대차수소이직접급출보반경적계산치,여고계보반경상하계적방법상비,전자경정학;대20계지1500계적수궤구진내지전형적병태구진Hilbert구진,야이교소적질대차수득도정학결과.위보반경적직접계산제공료유효적신방법.
in the estimation of the spectral radius of non negative matrix, the method of direct calculation is less and more than that of the power method or diagonal similarity transformation instead of matrix factorization. Since matrix decomposition is the main technique of matrix computation, and the non negative matrix factorization has a unique visual interpretation, the method of calcu?lating the non negative matrix spectral radius is proposed. The convergence of the sequence is constructed, and the spectral radius of the sequence is convergent. Experimental results show that:for the same non negative matrix, the calculated values of the spec?tral radius are few, and the former is more accurate than the upper and lower bounds of the spectral radius. The 20 order to 1500 or?der of the random matrix and the typical ill matrix Hilbert matrix are also given. A new method is provided for the direct calculation of the spectral radius.
