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December  2020, 10(4): 511-520. doi: 10.3934/naco.2020048

Parameter-related projection-based iterative algorithm for a kind of generalized positive semidefinite least squares problem

 College of Mathematics and Informatics, Fujian Normal University, Fuzhou, 350007, P. R. China

Received  March 2020 Revised  September 2020 Published  September 2020

Fund Project: This work was supported by the National Natural Science Foundations of China (11301080, 11526053), Science Foundation of Fujian Province of China (2016J05003), the Foundation of the Education Department of Fujian Province of China (JA15106), and the Project of Nonlinear analysis and its applications (IRTL1206)

A projection-based iterative algorithm, which is related to a single parameter (or the multiple parameters), is proposed to solve the generalized positive semidefinite least squares problem introduced in this paper. The single parameter (or the multiple parameters) projection-based iterative algorithms converges to the optimal solution under certain condition, and the corresponding numerical results are shown too.

Citation: Chengjin Li. Parameter-related projection-based iterative algorithm for a kind of generalized positive semidefinite least squares problem. Numerical Algebra, Control & Optimization, 2020, 10 (4) : 511-520. doi: 10.3934/naco.2020048
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Comparing of Algorithm 2.4 and Algorithm 3.2
 Parameters Spending time Parameters Spending time $(m,n,p,(r))$ $type$ $tim1$ $tim2$ $(m,n,p,(r))$ $type$ $tim1$ $tim2$ (71, 65, 67) T1 62.1 15.6 (59, 8, 30) T1 0.017 0.016 (53, 39, 48) 2.13 1.95 (103, 61, 85) 1.82 1.09 (101, 33, 61) 0.25 0.19 (102, 78, 90) 8.95 5.61 (102, 19, 95) 0.040 0.039 (93, 20, 92) 0.041 0.038 (66, 48, 53) 10.1 3.28 (58, 18, 45) 0.05 0.05 (62, 4, 38) T2 0.009 0.008 (49, 41, 42) T2 115.6 8.67 (71, 11, 24) 0.04 0.02 (94, 44, 92) 0.94 0.28 (92, 43, 64) 1.99 0.45 (98, 19, 93) 0.05 0.03 (93, 7, 48) 0.014 0.012 (73, 4, 30) 0.008 0.007 (86, 64, 72) 32.9 3.99 (78, 39, 62) 1.54 0.34 (94, 16, 85, (6)) T3 0.03 0.02 (91, 43, 83, (21)) T3 0.90 0.20 (60, 36, 53, (25)) 1.18 0.28 (54, 11, 24, (9)) 0.04 0.02 (31, 8, 10, (7)) 0.12 0.03 (86, 9, 83, (1)) 0.019 0.015 (78, 55, 69, (7)) 20.7 0.77 (97, 17, 33, (15)) 0.08 0.04 (98, 43, 51, (3)) 10.3 0.44 (42, 10, 36, (9)) 0.023 0.019
 Parameters Spending time Parameters Spending time $(m,n,p,(r))$ $type$ $tim1$ $tim2$ $(m,n,p,(r))$ $type$ $tim1$ $tim2$ (71, 65, 67) T1 62.1 15.6 (59, 8, 30) T1 0.017 0.016 (53, 39, 48) 2.13 1.95 (103, 61, 85) 1.82 1.09 (101, 33, 61) 0.25 0.19 (102, 78, 90) 8.95 5.61 (102, 19, 95) 0.040 0.039 (93, 20, 92) 0.041 0.038 (66, 48, 53) 10.1 3.28 (58, 18, 45) 0.05 0.05 (62, 4, 38) T2 0.009 0.008 (49, 41, 42) T2 115.6 8.67 (71, 11, 24) 0.04 0.02 (94, 44, 92) 0.94 0.28 (92, 43, 64) 1.99 0.45 (98, 19, 93) 0.05 0.03 (93, 7, 48) 0.014 0.012 (73, 4, 30) 0.008 0.007 (86, 64, 72) 32.9 3.99 (78, 39, 62) 1.54 0.34 (94, 16, 85, (6)) T3 0.03 0.02 (91, 43, 83, (21)) T3 0.90 0.20 (60, 36, 53, (25)) 1.18 0.28 (54, 11, 24, (9)) 0.04 0.02 (31, 8, 10, (7)) 0.12 0.03 (86, 9, 83, (1)) 0.019 0.015 (78, 55, 69, (7)) 20.7 0.77 (97, 17, 33, (15)) 0.08 0.04 (98, 43, 51, (3)) 10.3 0.44 (42, 10, 36, (9)) 0.023 0.019
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