闭凸集约束下线性矩阵方程求解的松弛交替投影算法

doi:10.12386/A2014sxxb0003

鏁板瀛︽姤鈥衡�� 2014, Vol. 57 鈥衡�� Issue (1): 17-34.DOI: 10.12386/A2014sxxb0003

鈥� 璁烘枃鈥� 涓婁竴绡� 涓嬩竴绡�

闂嚫闆嗙害鏉熶笅绾挎�х煩闃垫柟绋嬫眰瑙ｇ殑鏉惧紱浜ゆ浛鎶曞奖绠楁硶

鏉庡В鑺�¹, 鑳￠敗鐐�², 寮犵²

1. 妗傛灄鐢靛瓙绉戞妧澶у鏁板涓庤绠楃瀛﹀闄� 妗傛灄 541004;
2. 婀栧崡澶у鏁板涓庤閲忕粡娴庡闄� 闀挎矙 410082

鏀剁鏃ユ湡:2011-11-07 淇洖鏃ユ湡:2013-03-22 鍑虹増鏃ユ湡:2014-01-15 鍙戝竷鏃ユ湡:2014-01-15
鍩洪噾璧勫姪:
鍥藉鑷劧绉戝鍩洪噾璧勫姪椤圭洰锛�11226323锛�11101100锛�11261014锛夛紱骞胯タ鑷劧绉戝鍩洪噾璧勫姪椤圭洰锛�2013GXNSFBA019009锛�2012GXNSFBA053006锛�

Relaxed Alternating Projection Method for Solving Linear Matrix Equation Problem under Closed Convex Constraint

Jiao Fen LI¹, Xi Yan HU², Lei ZHANG²

1. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China;
2. College of Mathematics and Econometrics, Hunan University, Changsha 410082, P. R. China

Received:2011-11-07 Revised:2013-03-22 Online:2014-01-15 Published:2014-01-15

鎽樿/Abstract

鎽樿锛� 鐮旂┒绾挎�х煩闃垫柟绋�AXB=C鍦ㄩ棴鍑搁泦鍚�R绾︽潫涓嬬殑鏁板�艰凯浠ｈВ娉�. 鎵�鑰冭檻鐨勯棴鍑搁泦鍚�R涓�(1)鏈夌晫鐭╅樀闆嗗悎, (2)Q-姝ｅ畾鐭╅樀闆嗗悎鍜�(3)鐭╅樀涓嶇瓑寮忚В闆嗗悎.鏋勯�犳澗寮涗氦鏇挎姇褰辩畻娉曟眰瑙ｄ笂杩伴棶棰�,骞剁敤绠楀瓙鐞嗚璇佹槑浜嗙敱璇ョ畻娉曠敓鎴愮殑搴忓垪鍏锋湁寮辨敹鏁涙��.缁欏嚭浜嗙煩闃垫柟绋�AXB=C姹傚绉伴潪璐熻В鍜屽绉板崐姝ｅ畾瑙ｇ殑鏁板�肩畻渚�,澶ч噺鏁板�煎疄楠岄獙璇佷簡璇ョ畻娉曠殑鍙鎬у拰楂樻晥鎬�,骞惰鏄庤绠楁硶涓庝氦鏇挎姇褰辩畻娉曞拰璋辨姇褰辨搴︾畻娉曟瘮杈冨湪杩唬鏁堢巼涓婄殑鏄庢樉浼樺娍.

鍏抽敭璇�: 鐭╅樀鏂圭▼, 浜ゆ浛鎶曞奖绠楁硶, 鏉惧紱浜ゆ浛鎶曞奖绠楁硶

Abstract: We discuss the existing relaxed alternating projection method for solving the linear matrix equation AXB=C under some closed convex constraints to X. The considered closed convex constrained set, denoted by R, is (1) the set of bounded matrices, (2) the set of Q-positive definite matrices, (3) the solution set of a linear matrix inequality. We prove the weak convergence of the matrix sequence generated by the proposed algorithm, and present some numerical examples for solving AXB=C under symmetric nonnegative and symmetric positive semidefinite matrices constraint to illustrate the feasibility and efficiency of the proposed algorithm, and to show its clear superiority comparing with alternating projection method and spectral projected gradient method.

Key words: linear matrix equation, alternating projection method, relaxed alternating projection method

涓浘鍒嗙被鍙�:

15A24

鏉庡В鑺�, 鑳￠敗鐐�, 寮犵. 闂嚫闆嗙害鏉熶笅绾挎�х煩闃垫柟绋嬫眰瑙ｇ殑鏉惧紱浜ゆ浛鎶曞奖绠楁硶[J]. 鏁板瀛︽姤, 2014, 57(1): 17-34.

Jiao Fen LI, Xi Yan HU, Lei ZHANG. Relaxed Alternating Projection Method for Solving Linear Matrix Equation Problem under Closed Convex Constraint[J]. Acta Mathematica Sinica, Chinese Series, 2014, 57(1): 17-34.

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閾炬帴鏈枃: https://actamath.cjoe.ac.cn/Jwk_sxxb_cn/CN/10.12386/A2014sxxb0003

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鍙傝�冩枃鐚�

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闂嚫闆嗙害鏉熶笅绾挎�х煩闃垫柟绋嬫眰瑙ｇ殑鏉惧紱浜ゆ浛鎶曞奖绠楁硶

Relaxed Alternating Projection Method for Solving Linear Matrix Equation Problem under Closed Convex Constraint

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