On the sensitivity of multiple eigenvalues of quadratic eigenvalue problems dependent on several parameters 多參數(shù)二次特征值問題重特征值的靈敏度分析
On these grounds, the sensitivity of semisimple multiple eigenvalues of generalized eigenvalue problems is defined, and the sensitive elements of matrix pairs can be determined 以所得結(jié)論為基礎(chǔ),定義了廣義特征值問題半單重特征值的靈敏度,給出了確定矩陣對(duì)中敏感元素的方法。
Following from the results of sensitivity analysis of standard eigenvalue problems, the differentiability of semisimple multiple eigenvalues of nonsymmetric generalized eigenvalue problems is proved, and the derivatives of semisimple multiple eigenvalues and the series expansions of the corresponding eigenvectors are obtained 摘要以標(biāo)準(zhǔn)特征值問題靈敏度分析的有關(guān)結(jié)論為基礎(chǔ),證明了單參數(shù)非對(duì)稱廣義特征值問題半單重特征值的可微性,給出了特征值導(dǎo)數(shù)的表達(dá)式和特征向量的級(jí)數(shù)展開式。
Following from the results of sensitivity analysis of standard eigenvalue problems, the differentiability of semisimple multiple eigenvalues of nonsymmetric generalized eigenvalue problems is proved, and the derivatives of semisimple multiple eigenvalues and the series expansions of the corresponding eigenvectors are obtained 摘要以標(biāo)準(zhǔn)特征值問題靈敏度分析的有關(guān)結(jié)論為基礎(chǔ),證明了單參數(shù)非對(duì)稱廣義特征值問題半單重特征值的可微性,給出了特征值導(dǎo)數(shù)的表達(dá)式和特征向量的級(jí)數(shù)展開式。