Hermitian matrix of the two types of non-reflexive

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Hermitian matrix of the two types of non-reflexive inverse problem

Least Squares Solutions of Eigenvalue LJ]. Computational Mathematics, 2001,23 (2) :209-218. [33 Sheng Yanping,[link widoczny dla zalogowanych], Xie Dongxiu. Double anti-symmetric matrix conditions for the existence of Solutions [J]. Numerical Methods and Computer Applications, 2002,23 (2) :111-120. E43 Xiedong Xiu,[link widoczny dla zalogowanych], Ping Liao. Class of Antisymmetric Symmetric squares solutions of inverse problems [J]. Numerical Methods and Computer Applications, 2003,24 (4) :304-313. [5] Mr Hu Yan, Zhang Lei,[link widoczny dla zalogowanych], Zhou Fu Zhao. Symmetric orthogonal symmetric matrix inverse eigenvalue problem [J]. Computational Mathematics, 2003,25 (1) :13-22. [6] Dai Hua. Symmetric Orthogonal least squares solution of inverse problems [J]. Computational Mathematics, 2003,25 (1) :59-66. [7] ZhongzhoZhang,[link widoczny dla zalogowanych], XiyanHu, LeiZhang. Least-squaressolutionsofinverseproblemforHermitiangeneralizedHamiltonianmatrices [J]. AppliedMathematicsLetters, 2004,17 ( Cool

:303-308. [8] ZhenYunPeng. TheinverseeigenvalueproblemforHermitiananti-reflexivematricesanditsapproximation [J]. AppliedMathematicsandComputation, 2005,162 (3) :1377-1389. SG_LB �� D1-2SGBD1-2l2O of Mathematics, Vol 25 TwoKindsofInverseProblemsforHermitianAnti-reflexiveMatricesLIANGJ one by one A, A �� C Thefollowingthreeproblemsareconsideredinthispaper. ProblemI: Givenx, B ��, findAEHAdn ~ n, suchthatllAx-BIl-rain. ProblemII: GivenXEnXm, BEC, findAEHAJ,[link widoczny dla zalogowanych], suchthatXAX-B. ForProblemI, ageneralexpressionoftheleastsquaresolutionisobtainedbyusingthesingularvaluedecompositionmethod. ForProblem1I, thenecessaryandsufficientconditionsandageneralexpressionsolutionarediscussedbyusingthegeneralizedsingularvaluedecompositionmethod. Atlast, wederivetherepresentationoftheuniqueoptimalapproximationsfromthesolutionsofproblemsIand1I. Keywords: inverseproblemofmatrix; Hermitiananti-reflexivematrix; Frobeniusnorm; generalsingularvaluedecomposition