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A new class of positive semi-definite tensors
Convergence analysis of a new iterative algorithm for solving split variational inclusion problems
College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing 400067, China |
The split variational inclusion problem (SVIP) has been extensively studied and applied in real-world problems such as intensity-modulated radiation therapy (IMRT) and in sensor networks and in computerized tomography and data compression. Inspired by the works of L$\acute{o}$pez et al.$[24]$, Byrne et al.[
References:
[1] |
Q. H. Ansari and A. Rehan,
Iterative methods for generalized split feasibility problems in Banach spaces, Carpathian Journal of Mathematics, 33 (2017), 9-26.
|
[2] |
Q. H. Ansari and A. Rehan, Split feasibility and fixed point problems, in Nonlinear Analysis: Approximation Theory, Optimization and Applications, Edited by Q.H. Ansari, Birkhäuser, Springer, New Delhi, Heidelberg, New York, Dordrecht, London, (2014), 281-322. |
[3] |
Q. H. Ansari, A. Rehan and C. F. Wen, Implicit and explicit algorithms for split common fixed point problems, Journal of Nonlinear and Convex Analysis, 17 (2016), 1381-1397. |
[4] |
Q. H. Ansari, A. Rehan and J. C. Yao,
Split feasibility and fixed point problems for asymptotically k-strict pseudo-contractive mappings in intermediate sense, Fixed Point Theory, 18 (2017), 57-68.
doi: 10.24193/fpt-ro.2017.1.06. |
[5] |
J. P. Aubin, Optima and Equilibria: An Introduction to Nonlinear Analysis, Springer, 1993.
doi: 10.1007/978-3-662-02959-6. |
[6] |
J. B. Baillon, R. E. Bruck and S. Reich, On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces, Hou Journal of Mathematics, 4 (1978), 1-9. |
[7] |
F. E. Browder and W. V. Petryshyn,
The solution by iteration of nonlinear functional equations in Banach spaces, Bulletin of the American Mathematical Society, 72 (1966), 571-575.
doi: 10.1090/S0002-9904-1966-11544-6. |
[8] |
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441-453.
doi: 10.1088/0266-5611/18/2/310. |
[9] |
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120.
doi: 10.1088/0266-5611/20/1/006. |
[10] |
C. Byrne, Y. Censor, A. Gibali and S. Reich,
Weak and strong convergence of algorithms for the split common null point problem, J. Nonlinear ConvexAnal, 13 (2012), 759-775.
|
[11] |
L. C. Ceng, Q. H. Ansari and J. C. Yao, An extragradient method for solving split feasibility and fixed point problems, Comput. Math. Appl., 64 (2012), 633-642.
doi: 10.1016/j.camwa.2011.12.074. |
[12] |
L. C. Ceng, Q. H. Ansari and J. C. Yao, Mann type iterative methods for finding a common solution of split feasibility and fixed point problems, Positivity, 16 (2012), 471-495.
doi: 10.1007/s11117-012-0174-8. |
[13] |
Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algor., 8 (1994), 221-239.
doi: 10.1007/BF02142692. |
[14] |
Y. Censor, T.Bortfeld, B. Martin and A. Trofimov, A unified approach for inversion problems in intensity modulated radiation therapy, Phy. Med. Biol., 51 (2003), 2353-2365. Google Scholar |
[15] |
Y. Censor, A.Gibali and S. Reich, Algorithms for the split variational inequality problem, Numer. Algor., 59 (2012), 301-323.
doi: 10.1007/s11075-011-9490-5. |
[16] |
Y. Dang and Y. Gao, The strong convergence of a KM-CQ-like algorithm for a split feasibility problem, Inverse Problems, 27 (2011), ID 015007, 9pp.
doi: 10.1088/0266-5611/27/1/015007. |
[17] |
J. Deepho and P. Kumam, The hybrid steepest descent method for split variational inclusion and constrained convex minimization problems, Abstract and Applied Analysis, 2014 (2014), Article ID 365203, 13pp.
doi: 10.1155/2014/365203. |
[18] |
A. Gibali, L. W. Liu and Y. C. Tang, Note on the modified relaxation CQ algorithm for the split feasibility problem, Optim. Lett., 12 (2018), 817-830.
doi: 10.1007/s11590-017-1148-3. |
[19] |
A. Gibali, D. T. Mai and T. V. Nguyen, A new relaxed CQ algorithm for solving Split Feasibility Problems in Hilbert spaces and its applications, J. Indus. Manag. Optim., 2018 (2018), 1-25. Google Scholar |
[20] |
B. Halpern, Fixed points of nonexpanding maps, Bulletin of the American Mathematical Society, 73 (1967), 957-961.
doi: 10.1090/S0002-9904-1967-11864-0. |
[21] |
S. Ishikawa,
Fixed points and iteration of a nonexpansive mapping in Banach space, Processing of the American Mathematical Society, 59 (1976), 65-71.
doi: 10.1090/S0002-9939-1976-0412909-X. |
[22] |
K. R. Kazmi and S. H. Rizvi,
An iterative method for split variational inclusion problem and fixed point problem for a nonexpansive mapping, Optim. Lett., 8 (2014), 1113-1124.
doi: 10.1007/s11590-013-0629-2. |
[23] |
M. A. Krasnosel'skii,
Two remarks on the method of successive approximations(in Russion), Uspekhi Mathematicheskikh Nauk, 10 (1955), 123-127.
|
[24] |
G. López, V. Martin-Marquez and H. K. Xu, Solving the split feasibilty problem without prior knowledge of matrix norms, Inverse Problems, 28 (2012), ID085004, 18pp.
doi: 10.1088/0266-5611/28/8/085004. |
[25] |
P. E. Mainge, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal., 16 (2008), 899-912.
doi: 10.1007/s11228-008-0102-z. |
[26] |
P. E. Mainge, Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 325 (2007), 469-479.
doi: 10.1016/j.jmaa.2005.12.066. |
[27] |
W. R. Mann, Mean value methods in iteration, Processing of the American Mathematical Society, 4 (1953), 506-510.
doi: 10.1090/S0002-9939-1953-0054846-3. |
[28] |
A. Moudafi, Split monotone variational inclusions, J. Optim. Theory Appl, 150 (2011), 275-283.
doi: 10.1007/s10957-011-9814-6. |
[29] |
A. Moudafi and B. S. Thakur, Solving proximal split feasibilty problem without prior knowledge of matrix norms, Optimization Letters, 8 (2014), 2099-2110.
doi: 10.1007/s11590-013-0708-4. |
[30] |
A. Moudafi and A. Gibali, $l_1$-$l_2$ regularization of split feasibility problems, Numer. Algor., 78 (2018), 739-757.
doi: 10.1007/s11075-017-0398-6. |
[31] |
A. Moudafi, The split common fixed point problem for demicontractive mappings, Inverse Problems, 26 (2010), 055007, 6 pp.
doi: 10.1088/0266-5611/26/5/055007. |
[32] |
T. L. N. Nguyen and Y. Shin, Deterministic sensing matrices in compressive sensing: A survey, Sci. World J., 2013 (2013), 1-6. Google Scholar |
[33] |
Y. Shehu and O. S. Iyiola, Convergence analysis for the proximal split feasibiliy problem using an inertial extrapolation term method, J. Fixed Point Theory Appl., 19 (2017), 2843-2510.
doi: 10.1007/s11784-017-0435-z. |
[34] |
K. Sitthithakerngkiet, J. Deepho and P. Kumam, Convergence analysis of a general iterative algorithm for finding a common solution o split variational inclusion and optimization problems, Numer. Algorithms, 79 (2018), 801-824.
doi: 10.1007/s11075-017-0462-2. |
[35] |
K. Sitthithakerngkiet, J. Deepho and P. Kumam,
A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems, Applied Mathematics and Computation, 250 (2015), 986-1001.
doi: 10.1016/j.amc.2014.10.130. |
[36] |
T. Suzuki, A sufficient and necesssary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings, Processing of the American Mathematical Society, 135 (2007), 99-106.
doi: 10.1090/S0002-9939-06-08435-8. |
[37] |
H. K. Xu, Iterative algorithms for nonlinear operators, J. Lond. Math. Soc., 66 (2002), 240-256.
doi: 10.1112/S0024610702003332. |
[38] |
Q. Yang, The relaxed CQ algorithm for solving the split feasibility problem, Inverse Problems, 20 (2004), 1261-1266.
doi: 10.1088/0266-5611/20/4/014. |
[39] |
L. Yang and F. H. Zhao, General split variational inclusion problem in hilbert spaces, Abstract and Applied Analysis, 2014 (2014), Article ID 816035, 8pp.
doi: 10.1155/2014/816035. |
show all references
References:
[1] |
Q. H. Ansari and A. Rehan,
Iterative methods for generalized split feasibility problems in Banach spaces, Carpathian Journal of Mathematics, 33 (2017), 9-26.
|
[2] |
Q. H. Ansari and A. Rehan, Split feasibility and fixed point problems, in Nonlinear Analysis: Approximation Theory, Optimization and Applications, Edited by Q.H. Ansari, Birkhäuser, Springer, New Delhi, Heidelberg, New York, Dordrecht, London, (2014), 281-322. |
[3] |
Q. H. Ansari, A. Rehan and C. F. Wen, Implicit and explicit algorithms for split common fixed point problems, Journal of Nonlinear and Convex Analysis, 17 (2016), 1381-1397. |
[4] |
Q. H. Ansari, A. Rehan and J. C. Yao,
Split feasibility and fixed point problems for asymptotically k-strict pseudo-contractive mappings in intermediate sense, Fixed Point Theory, 18 (2017), 57-68.
doi: 10.24193/fpt-ro.2017.1.06. |
[5] |
J. P. Aubin, Optima and Equilibria: An Introduction to Nonlinear Analysis, Springer, 1993.
doi: 10.1007/978-3-662-02959-6. |
[6] |
J. B. Baillon, R. E. Bruck and S. Reich, On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces, Hou Journal of Mathematics, 4 (1978), 1-9. |
[7] |
F. E. Browder and W. V. Petryshyn,
The solution by iteration of nonlinear functional equations in Banach spaces, Bulletin of the American Mathematical Society, 72 (1966), 571-575.
doi: 10.1090/S0002-9904-1966-11544-6. |
[8] |
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441-453.
doi: 10.1088/0266-5611/18/2/310. |
[9] |
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120.
doi: 10.1088/0266-5611/20/1/006. |
[10] |
C. Byrne, Y. Censor, A. Gibali and S. Reich,
Weak and strong convergence of algorithms for the split common null point problem, J. Nonlinear ConvexAnal, 13 (2012), 759-775.
|
[11] |
L. C. Ceng, Q. H. Ansari and J. C. Yao, An extragradient method for solving split feasibility and fixed point problems, Comput. Math. Appl., 64 (2012), 633-642.
doi: 10.1016/j.camwa.2011.12.074. |
[12] |
L. C. Ceng, Q. H. Ansari and J. C. Yao, Mann type iterative methods for finding a common solution of split feasibility and fixed point problems, Positivity, 16 (2012), 471-495.
doi: 10.1007/s11117-012-0174-8. |
[13] |
Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algor., 8 (1994), 221-239.
doi: 10.1007/BF02142692. |
[14] |
Y. Censor, T.Bortfeld, B. Martin and A. Trofimov, A unified approach for inversion problems in intensity modulated radiation therapy, Phy. Med. Biol., 51 (2003), 2353-2365. Google Scholar |
[15] |
Y. Censor, A.Gibali and S. Reich, Algorithms for the split variational inequality problem, Numer. Algor., 59 (2012), 301-323.
doi: 10.1007/s11075-011-9490-5. |
[16] |
Y. Dang and Y. Gao, The strong convergence of a KM-CQ-like algorithm for a split feasibility problem, Inverse Problems, 27 (2011), ID 015007, 9pp.
doi: 10.1088/0266-5611/27/1/015007. |
[17] |
J. Deepho and P. Kumam, The hybrid steepest descent method for split variational inclusion and constrained convex minimization problems, Abstract and Applied Analysis, 2014 (2014), Article ID 365203, 13pp.
doi: 10.1155/2014/365203. |
[18] |
A. Gibali, L. W. Liu and Y. C. Tang, Note on the modified relaxation CQ algorithm for the split feasibility problem, Optim. Lett., 12 (2018), 817-830.
doi: 10.1007/s11590-017-1148-3. |
[19] |
A. Gibali, D. T. Mai and T. V. Nguyen, A new relaxed CQ algorithm for solving Split Feasibility Problems in Hilbert spaces and its applications, J. Indus. Manag. Optim., 2018 (2018), 1-25. Google Scholar |
[20] |
B. Halpern, Fixed points of nonexpanding maps, Bulletin of the American Mathematical Society, 73 (1967), 957-961.
doi: 10.1090/S0002-9904-1967-11864-0. |
[21] |
S. Ishikawa,
Fixed points and iteration of a nonexpansive mapping in Banach space, Processing of the American Mathematical Society, 59 (1976), 65-71.
doi: 10.1090/S0002-9939-1976-0412909-X. |
[22] |
K. R. Kazmi and S. H. Rizvi,
An iterative method for split variational inclusion problem and fixed point problem for a nonexpansive mapping, Optim. Lett., 8 (2014), 1113-1124.
doi: 10.1007/s11590-013-0629-2. |
[23] |
M. A. Krasnosel'skii,
Two remarks on the method of successive approximations(in Russion), Uspekhi Mathematicheskikh Nauk, 10 (1955), 123-127.
|
[24] |
G. López, V. Martin-Marquez and H. K. Xu, Solving the split feasibilty problem without prior knowledge of matrix norms, Inverse Problems, 28 (2012), ID085004, 18pp.
doi: 10.1088/0266-5611/28/8/085004. |
[25] |
P. E. Mainge, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal., 16 (2008), 899-912.
doi: 10.1007/s11228-008-0102-z. |
[26] |
P. E. Mainge, Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 325 (2007), 469-479.
doi: 10.1016/j.jmaa.2005.12.066. |
[27] |
W. R. Mann, Mean value methods in iteration, Processing of the American Mathematical Society, 4 (1953), 506-510.
doi: 10.1090/S0002-9939-1953-0054846-3. |
[28] |
A. Moudafi, Split monotone variational inclusions, J. Optim. Theory Appl, 150 (2011), 275-283.
doi: 10.1007/s10957-011-9814-6. |
[29] |
A. Moudafi and B. S. Thakur, Solving proximal split feasibilty problem without prior knowledge of matrix norms, Optimization Letters, 8 (2014), 2099-2110.
doi: 10.1007/s11590-013-0708-4. |
[30] |
A. Moudafi and A. Gibali, $l_1$-$l_2$ regularization of split feasibility problems, Numer. Algor., 78 (2018), 739-757.
doi: 10.1007/s11075-017-0398-6. |
[31] |
A. Moudafi, The split common fixed point problem for demicontractive mappings, Inverse Problems, 26 (2010), 055007, 6 pp.
doi: 10.1088/0266-5611/26/5/055007. |
[32] |
T. L. N. Nguyen and Y. Shin, Deterministic sensing matrices in compressive sensing: A survey, Sci. World J., 2013 (2013), 1-6. Google Scholar |
[33] |
Y. Shehu and O. S. Iyiola, Convergence analysis for the proximal split feasibiliy problem using an inertial extrapolation term method, J. Fixed Point Theory Appl., 19 (2017), 2843-2510.
doi: 10.1007/s11784-017-0435-z. |
[34] |
K. Sitthithakerngkiet, J. Deepho and P. Kumam, Convergence analysis of a general iterative algorithm for finding a common solution o split variational inclusion and optimization problems, Numer. Algorithms, 79 (2018), 801-824.
doi: 10.1007/s11075-017-0462-2. |
[35] |
K. Sitthithakerngkiet, J. Deepho and P. Kumam,
A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems, Applied Mathematics and Computation, 250 (2015), 986-1001.
doi: 10.1016/j.amc.2014.10.130. |
[36] |
T. Suzuki, A sufficient and necesssary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings, Processing of the American Mathematical Society, 135 (2007), 99-106.
doi: 10.1090/S0002-9939-06-08435-8. |
[37] |
H. K. Xu, Iterative algorithms for nonlinear operators, J. Lond. Math. Soc., 66 (2002), 240-256.
doi: 10.1112/S0024610702003332. |
[38] |
Q. Yang, The relaxed CQ algorithm for solving the split feasibility problem, Inverse Problems, 20 (2004), 1261-1266.
doi: 10.1088/0266-5611/20/4/014. |
[39] |
L. Yang and F. H. Zhao, General split variational inclusion problem in hilbert spaces, Abstract and Applied Analysis, 2014 (2014), Article ID 816035, 8pp.
doi: 10.1155/2014/816035. |








n | ||
0 | (1, -1, 2) | 2.4490 |
1 | (0.3331, -0.4494, -1.31740) | 1.4313 |
2 | (0.1301, -0.2359, -1.0027) | 1.0383 |
3 | (0.0555, -0.1328, -0.8102) | 0.8229 |
4 | (0.0251, -0.0765, -0.6615) | 0.6664 |
5 | (0.0120, -0.0443, -0.5355) | 0.5374 |
... | ||
10 | (0.0010, -0.0035, -0.1571) | 0.1572 |
20 | (0.0001, -0.0001, -0.0106) | 0.0106 |
30 | (0.0000, 0.0000, -0.00072) | 7.1865e-04 |
36 | (0.0000, 0.0000, -0.0001) | 1.4345e-04 |
37 | (0.0000, 0.0000, -0.0001) | 1.097e-04 |
38 | (0.0000, 0.0000, 0.0000) | 0.0000 |
n | ||
0 | (1, -1, 2) | 2.4490 |
1 | (0.3331, -0.4494, -1.31740) | 1.4313 |
2 | (0.1301, -0.2359, -1.0027) | 1.0383 |
3 | (0.0555, -0.1328, -0.8102) | 0.8229 |
4 | (0.0251, -0.0765, -0.6615) | 0.6664 |
5 | (0.0120, -0.0443, -0.5355) | 0.5374 |
... | ||
10 | (0.0010, -0.0035, -0.1571) | 0.1572 |
20 | (0.0001, -0.0001, -0.0106) | 0.0106 |
30 | (0.0000, 0.0000, -0.00072) | 7.1865e-04 |
36 | (0.0000, 0.0000, -0.0001) | 1.4345e-04 |
37 | (0.0000, 0.0000, -0.0001) | 1.097e-04 |
38 | (0.0000, 0.0000, 0.0000) | 0.0000 |
n | ||||
0 | (13, -12, 25) | (4.4303, -5.5150, 17.4474) | 30.6268 | 18.8270 |
1 | (2.2152, -2.7575, 8.7237) | (0.9781, -1.4819, 6.3531) | 9.4135 | 6.5966 |
2 | (0.4328, -0.7128, 3.5425) | (0.2146, -0.4159, 2.6836) | 3.6393 | 2.7241 |
3 | (0.0883, -0.1959, 1.5783) | (0.0464, -0.1202, 1.2365) | 1.5928 | 1.2432 |
4 | (0.0180, -0.0560, 0.7595) | (0.0095, -0.0353, 0.6112) | 0.7617 | 0.6123 |
5 | (0.0033, -0.0162, 0.3900) | (0.0015, -0.0102, 0.3204) | 0.3904 | 0.3206 |
... | ||||
10 | (-0.0001, 0.0002, 0.0248) | (-0.0001, 0.0002, 0.0213) | 0.0248 | 0.0213 |
15 | (0.0000, 0.0000, 0.0037) | (0.0000, 0.0000, 0.0032) | 0.0037 | 0.0032 |
18 | (0.0000, 0.0000, 0.00093) | (0.0000, 0.0000, 0.00081) | 9.2969e-04 | 8.0753e-04 |
19 | (0.0000, 0.0000, 0.00059) | (0.0000, 0.0000, 0.00052) | 5.9324e-04 | 5.1575e-04 |
20 | (0.0000, 0.0000, 0.00038) | (0.0000, 0.0000, 0.0003) | 3.7973e-04 | 3.304e-04 |
21 | (0.0000, 0.0000, 0.0000) | (0.0000, 0.0000, 0.0000) | 0 | 0 |
n | ||||
0 | (13, -12, 25) | (4.4303, -5.5150, 17.4474) | 30.6268 | 18.8270 |
1 | (2.2152, -2.7575, 8.7237) | (0.9781, -1.4819, 6.3531) | 9.4135 | 6.5966 |
2 | (0.4328, -0.7128, 3.5425) | (0.2146, -0.4159, 2.6836) | 3.6393 | 2.7241 |
3 | (0.0883, -0.1959, 1.5783) | (0.0464, -0.1202, 1.2365) | 1.5928 | 1.2432 |
4 | (0.0180, -0.0560, 0.7595) | (0.0095, -0.0353, 0.6112) | 0.7617 | 0.6123 |
5 | (0.0033, -0.0162, 0.3900) | (0.0015, -0.0102, 0.3204) | 0.3904 | 0.3206 |
... | ||||
10 | (-0.0001, 0.0002, 0.0248) | (-0.0001, 0.0002, 0.0213) | 0.0248 | 0.0213 |
15 | (0.0000, 0.0000, 0.0037) | (0.0000, 0.0000, 0.0032) | 0.0037 | 0.0032 |
18 | (0.0000, 0.0000, 0.00093) | (0.0000, 0.0000, 0.00081) | 9.2969e-04 | 8.0753e-04 |
19 | (0.0000, 0.0000, 0.00059) | (0.0000, 0.0000, 0.00052) | 5.9324e-04 | 5.1575e-04 |
20 | (0.0000, 0.0000, 0.00038) | (0.0000, 0.0000, 0.0003) | 3.7973e-04 | 3.304e-04 |
21 | (0.0000, 0.0000, 0.0000) | (0.0000, 0.0000, 0.0000) | 0 | 0 |
DOL | Method | Step Size | Iter | CPU Time | |
Algorithm3.3 | 20 | 0.0698 | 1.2399e-05 | ||
Sitthithakerngkiet et al.[34] | 0.001 | 23 | 0.0763 | 7.4893e-06 | |
Byrne et al.[10] | 0.001 | 20 | 0.1187 | 4.7322e-05 | |
Algorithm3.3 | 25 | 0.0761 | 1.3826e-06 | ||
Sitthithakerngkiet et al.[34] | 0.001 | 219 | 0.0924 | 5.2309e-07 | |
Byrne et al.[10] | 0.001 | 24 | 0.1141 | 3.7345e-06 | |
Algorithm3.3 | 31 | 0.081 | 1.0539e-07 | ||
Sitthithakerngkiet et al.[34] | 0.001 | 2172 | 0.162 | 5.2141e-08 | |
Byrne et al.[10] | 0.001 | 27 | 0.1154 | 5.5604e-07 |
DOL | Method | Step Size | Iter | CPU Time | |
Algorithm3.3 | 20 | 0.0698 | 1.2399e-05 | ||
Sitthithakerngkiet et al.[34] | 0.001 | 23 | 0.0763 | 7.4893e-06 | |
Byrne et al.[10] | 0.001 | 20 | 0.1187 | 4.7322e-05 | |
Algorithm3.3 | 25 | 0.0761 | 1.3826e-06 | ||
Sitthithakerngkiet et al.[34] | 0.001 | 219 | 0.0924 | 5.2309e-07 | |
Byrne et al.[10] | 0.001 | 24 | 0.1141 | 3.7345e-06 | |
Algorithm3.3 | 31 | 0.081 | 1.0539e-07 | ||
Sitthithakerngkiet et al.[34] | 0.001 | 2172 | 0.162 | 5.2141e-08 | |
Byrne et al.[10] | 0.001 | 27 | 0.1154 | 5.5604e-07 |
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