In this paper, we further generalize the technique for constructing the normal （or pos- itive definite） and skew-Hermitian splitting iteration method for solving large sparse non- Hermitian positive definite system ...In this paper, we further generalize the technique for constructing the normal （or pos- itive definite） and skew-Hermitian splitting iteration method for solving large sparse non- Hermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting （PPS） methods, and prove that the sequence produced by the PPS method con- verges unconditionally to the unique solution of the system. Moreover, we propose two kinds of typical practical choices of the PPS method and study the upper bound of the spectral radius of the iteration matrix. In addition, we show the optimal parameters such that the spectral radius achieves the minimum under certain conditions. Finally, some numerical examples are given to demonstrate the effectiveness of the considered methods.展开更多
For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matr...For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matrix is a positive definite matrix or a positive semi-definite matrix, respectively. The advantages of the new methods are that they can solve the large scale stochastic linear complementarity problem, and spend less computational time. Numerical results show that the new methods are efficient and suitable for solving the large scale problems.展开更多
By presenting a counterexample, the author of paper （ZHAO Li-feng. J. Math. Res. Exposition, 2007, 27（4）： 949-954） declared that some assertions in papers of LU Yun-xia, ZHANG Shu-qing （J. Math. Res. Exposition,...By presenting a counterexample, the author of paper （ZHAO Li-feng. J. Math. Res. Exposition, 2007, 27（4）： 949-954） declared that some assertions in papers of LU Yun-xia, ZHANG Shu-qing （J. Math. Res. Exposition, 1999, 19（3）： 598-600）, HE Gan-tong （J. Math. Res. Exposition, 2002, 22（1）： 79-82） and YUAN Hui-ping （J. Math. Res. Exposition, 2001, 21（3）： 464-468） are wrong. In this note, we point out that the counterexample is wrong. Further discussion on these assertions and some related results are also given.展开更多
A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more strin...A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more stringent than the optimal bounds by Wolkowicz and Styan in specific cases.展开更多
文摘In this paper, we further generalize the technique for constructing the normal （or pos- itive definite） and skew-Hermitian splitting iteration method for solving large sparse non- Hermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting （PPS） methods, and prove that the sequence produced by the PPS method con- verges unconditionally to the unique solution of the system. Moreover, we propose two kinds of typical practical choices of the PPS method and study the upper bound of the spectral radius of the iteration matrix. In addition, we show the optimal parameters such that the spectral radius achieves the minimum under certain conditions. Finally, some numerical examples are given to demonstrate the effectiveness of the considered methods.
文摘For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matrix is a positive definite matrix or a positive semi-definite matrix, respectively. The advantages of the new methods are that they can solve the large scale stochastic linear complementarity problem, and spend less computational time. Numerical results show that the new methods are efficient and suitable for solving the large scale problems.
基金Supported by the Natural Science Foundation of Science and Technology Office of Guizhou Province (Grant No. J[2006]2002)
文摘By presenting a counterexample, the author of paper （ZHAO Li-feng. J. Math. Res. Exposition, 2007, 27（4）： 949-954） declared that some assertions in papers of LU Yun-xia, ZHANG Shu-qing （J. Math. Res. Exposition, 1999, 19（3）： 598-600）, HE Gan-tong （J. Math. Res. Exposition, 2002, 22（1）： 79-82） and YUAN Hui-ping （J. Math. Res. Exposition, 2001, 21（3）： 464-468） are wrong. In this note, we point out that the counterexample is wrong. Further discussion on these assertions and some related results are also given.
文摘A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more stringent than the optimal bounds by Wolkowicz and Styan in specific cases.
