One kind of inverse problem for the bisymmetric matrices 雙對稱矩陣的一類反問題
Bisymmetric nonnegative definite solution of matrix equations atx 的雙對稱非負定解
Inverse problem for general bisymmetric matrices 廣義雙對稱矩陣反問題
Least square solutions of matrix equation axb 范數雙對稱解
The generalized bisymmetric solution and generalized anti - bisymmetric solution of 的廣義雙對稱解與廣義雙反對稱解
D . x . xie , l . zhang and x . y . hu , least - square solutions of inverse eigenvalue probem of bisymmetric matrices , math . numer sinica , 1 ( 1999 ) 62 - 72 廖安平,謝冬秀,雙對稱非負定矩陣一類逆特征值問題的最小二乘解,計算數學, 23 : 2 ( 2001 ) 209 - 218
This ph . d . thesis - firstly considers the real asymmetric , real symmetric , bisym - metric , and symmetric and skew antisymmetric matrix extension problems constrained by the matrix inverse problem ax = b . and also considers , in the solution set , of the corresponding matrix extension problems , the optimal approximation solution to a given matrix a * . the necessary and sufficient conditions for the existence of and the expressions for the above problems are derived , and the numerical algorithm and examples to solve the problems are also given 首次提出并討論了矩陣反問題ax = b約束下實矩陣、實對稱矩陣、雙對稱矩陣和對稱次反對稱矩陣的擴充問題,討論了在其解集合中與給定矩陣a ~ *的最佳逼近問題,得到了問題的解存在的條件及通式的表示,給出求解問題的數值算法和數值例子。
In this thesis , we study some open problems and conjectures about the linear complementarity problem . it consists of the next three aspects : firstly , we study murthys " open problem whether the augmented matrix is a q0 - matrix for an arbitary square matrix a , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the graves algorithm can be used to solve linear complementarity problem with bisymmetry po - matrices ; secondly , we study murthys " conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix , we also study pang ' s conjecture , obtain two conditions when r0 - matrices and q - matrices are equivelent and some properties about e0 q - matrices ; lastly , we give a counterexample to prove danao ' s conjecture that if a is a po - matrix , a e " a p1 * is false , point out some mistakes of murthys in [ 20 ] , obtain when n = 2 or 3 , a e " a p1 * , i . e . the condition of theorem 3 . 2 of [ 25 ] that a p0 can be deleted and obtain a e " a is an almost e - matrix if a is a co - matrix or column sufficient matrix 本文分為三個部分,主要研究了線性互補問題的幾個相關的公開問題以及猜想: ( 1 )研究了murthy等在[ 2 ]中提出的公開問題,即對任意的矩陣a ,其擴充矩陣是否為q _ 0 -矩陣,給出了肯定的回答,得到充分矩陣的擴充矩陣是充分矩陣,并討論了graves算法,證明了若a是雙對稱的p _ 0 -矩陣時, lcp ( q , a )可由graves算法給出; ( 2 )研究了murthy等在[ 6 ]中提出關于半正定矩陣的猜想,給出了半正定矩陣的一些充分條件,并研究了pang ~ -猜想,得到了只r _ 0 -矩陣與q -矩陣的二個等價條件,以及e _ 0 q -矩陣的一些性質; ( 3 )研究了danao在[ 25 ]中提出的danao猜想,即,若a為p _ 0 -矩陣,則,我們給出了反例證明了此猜想當n 4時不成立,指出了murthy等在[ 20 ]中的一些錯誤,得到n = 2 , 3時,即[ 25 ]中定理3 . 2中a p _ 0的條件可以去掉。
Based on the properties of bisymmetric matrices , a class of constrained inverse eigenproblem and associated approximation problem for bisymmetric matrices were essentially decomposed into the same kind of subproblems for real symmetric matrices with smaller dimensions , and the solutions of the two problems were obtained by applying the conclusions of real symmetric matrices 摘要根據雙對稱矩陣的性質,將雙對稱矩陣的一類約束逆特征值問題及其逼近問題分解成具有較小階數的實對稱矩陣的同類子問題,然后利用實對稱矩陣的結果導出雙對稱矩陣的這兩個問題的解。