[1]
|
Z. Bai and M. Tao, Rigorous convergence analysis of alternating variable minimization with multiplier methods for quadratic programming problems with equality constraints, BIT Numerical Mathematics, 2016, 56(2), 399-422. doi: 10.1007/s10543-015-0563-z
CrossRef Google Scholar
|
[2]
|
H. H. Bauschke and J. M. Borwein, Dykstra's alternating projection algorithm for two sets, Journal of Approximation Theorem, 1994, 79(3), 418-443. doi: 10.1006/jath.1994.1136
CrossRef Google Scholar
|
[3]
|
A. Bjorck and G. D, Numerical methods in scientific computing, SIAM, Philadelphia, 2006.
Google Scholar
|
[4]
|
S. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Press, Oxford, 2004.
Google Scholar
|
[5]
|
S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Foundations and Trends in Machine Learning, 2011, 3(1), 1-122.
Google Scholar
|
[6]
|
J. Cai and G. Chen, An iterative algorithm for the least squares bisymmetric solutions of the matrix equations A1XB1 = C1, A2XB2 = C2, Mathematical and Computer Modelling, 2009, 50, 1237-1244. doi: 10.1016/j.mcm.2009.07.004
CrossRef Google Scholar
|
[7]
|
Y. Chen, Z. Peng and T. Zhou, LSQR iterative common symmetric solutions to matrix equations AXB = E and CXD = F, Applied Mathematics and Computation, 2010, 217, 230-236. doi: 10.1016/j.amc.2010.05.053
CrossRef Google Scholar
|
[8]
|
H. Dai and P. Lancaster, Linear matrix equations from an inverse problem of vibration theory, Linear Algebra and Its Applications, 1996, 246, 31-47. doi: 10.1016/0024-3795(94)00311-4
CrossRef Google Scholar
|
[9]
|
F. Deutsch, Best Approximation in Inner Produce Spaces, Springer, New York, 2001.
Google Scholar
|
[10]
|
X. Duan and C. Li, A new iterative algorithm for solving a class of matrix nearness problem, ISRN Computational Mathematics, 2012. DOI: 10.5402/2012/126908.
CrossRef Google Scholar
|
[11]
|
M. Friswell and J. Mottorshead, Finite Element Model Updating in Structure Dynamics, Kluwer Academic Publisher, Dodrecht, 1995.
Google Scholar
|
[12]
|
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Computers & Mathematics with Applications, 1976, 2(1), 17-40.
Google Scholar
|
[13]
|
N. Higham, Matrix Nearness Problems and Applications, Oxford University Press, London, 1989.
Google Scholar
|
[14]
|
Y. Ke and C. Ma, The unified frame of alternating direction method of multipliers for three classes of matrix equations arising in control theory: Alternating direction method of multipliers for matrix equations, Asian Journal of Control, 2018, 20(2), 437-454.
Google Scholar
|
[15]
|
C. Li, X. Duan and Z. Jiang, Dykstra's algorithm for the optimal approximate symmetric positive semidefinite solution of a class of matrix equations, Advances in Linear Algebra & Matrix Theory, 2016, 6, 1-10.
Google Scholar
|
[16]
|
J. V. Numann, Functional Operators, Princeton University Press, Princeton, 1950.
Google Scholar
|
[17]
|
C. Paige and M. A. Saunders, LSQR: an algorithm for sparse linear equations and sparse least squares, ACM Transaction on Mathematical Software, 1982, 8(1), 43-47. doi: 10.1145/355984.355989
CrossRef Google Scholar
|
[18]
|
Y. Peng, X. H and L. Zhang, An iterative method for symmetric solutions and optimal approximation solution of the system of matrix equations A1XB1 =C1, A2XB2 = C2, Applied Mathematics and Computation, 2006, 183(2), 1127- 1137. doi: 10.1016/j.amc.2006.05.124
CrossRef Google Scholar
|
[19]
|
Z. Peng, A matrix lsqr iterative method to solve matrix equation AXB = C, International Journal of Computer Mathematics, 2010, 87(8), 1820-1830. doi: 10.1080/00207160802516875
CrossRef Google Scholar
|
[20]
|
Z. Peng, Y. Fang, X. Xiao and D. Du, New algorithms to compute the nearness symmetric solution of the matrix equation, SpringerPlus, 2016, 5, 1005. doi: 10.1186/s40064-016-2416-x
CrossRef Google Scholar
|
[21]
|
M. Sarduvan, S. Ṣimṣek and H. Özdemir, ¨ On the matrix nearness problem for (skew-) symmetric matrices associated with the matrix equations (a1xb1, …, akxbk) = (c1, …, ck), Miskolc Mathematical Notes, 2016, 17, 635- 645. doi: 10.18514/MMN.2016.1435
CrossRef Google Scholar
|
[22]
|
J. Sun, Two kinds of inverse eigenvalue problems for real symmetric matrices, Mathematica Numerica Sinica, 1988, 3, 007.
Google Scholar
|
[23]
|
J. Zhang and J.G. Nagy, An alternating direction method of multipliers for the solution of matrix equations arising in inverse problems, Numerical Linear Algebra with Applications, 2017, 25(4), e2123.
Google Scholar
|