Some accelerated iterative algorithms for solving nonsymmetric algebraic Riccati equations arising in transport theory

References

• Z.-Z. Bai, X.-X. Guo and S.-F. Xu, Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations, Numer. Linear Algebra Appl. 13 (2006), pp. 655–674. doi: 10.1002/nla.500
   Web of Science ®Google Scholar
• Z.Z. Bai, Y.-H. Gao and L.-Z. Lu, Fast iterative schemes for nonsymmetric algebraic Riccati equations arising from transport theory, SIAM J. Sci. Comput. 30 (2008), pp. 804–818. doi: 10.1137/060675344
   Web of Science ®Google Scholar
• L. Bao, Y.-Q. Lin and Y.-M. Wei, A modified simple iterative method for nonsymmetric algebraic Riccati equations arising in transport theory, Appl. Math. Comput. 181 (2006), pp. 1499–1504.
   Web of Science ®Google Scholar
• D.-A. Bini, B. Iannazzo and F. Poloni, A fast Newton's method for a nonsymmetric algebraic Riccati equation, SIAM J. Matrix Anal. Appl. 30 (2008), pp. 276–290. doi: 10.1137/070681478
   Web of Science ®Google Scholar
• D.-A. Bini, B. Meini and F. Poloni, Fast solution of a certain Riccati equation through Cauchy-like matrices, Electron. T. Numer. Ana. 33 (2009), pp. 84–104.
   Web of Science ®Google Scholar
• P. Benner, H. Mena and J. Saak, On the parameter selection problem in the Newton-ADI iteration for large-scale Riccati equations, Electron. T. Numer. Ana. 29 (2008), pp. 136–149.
   Web of Science ®Google Scholar
• N. Dong, J. Jin and B. Yu, Convergence rates of a class of predictor-corrector iterations for the nonsymmetric algebraic Riccati equation arising in transport theory, Adv. Appl. Math. Mech. 9 (2017), pp. 944–963. doi: 10.4208/aamm.2015.m1277
   Web of Science ®Google Scholar
• Y.-H. Gao and Z.-Z. Bai, On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations, Numer. Linear Algebra Appl. 18 (2011), pp. 325–341. doi: 10.1002/nla.727
   Web of Science ®Google Scholar
• C.-H. Guo, Nonsymmetric algebraic Riccati equations and Wiener-Hopf factorization for M-matrices, SIAM J. Matrix Anal. Appl. 23 (2001), pp. 225–242. doi: 10.1137/S0895479800375680
   Web of Science ®Google Scholar
• C.-H. Guo and A.-J. Laub, On the iterative solution of a class of nonsymmetric algebraic Riccati equations, SIAM J. Matrix Anal. Appl. 22 (2000), pp. 376–391. doi: 10.1137/S089547989834980X
   Web of Science ®Google Scholar
• C.-H. Guo and W.-W. Lin, Convergence rates of some iterative methods for nonsymmetric algebraic Riccati equations arising in transport theory, Linear Algebra Appl. 432 (2010), pp. 283–291. doi: 10.1016/j.laa.2009.08.004
   Web of Science ®Google Scholar
• X.-X. Guo, W.-W. Lin and S.-F. Xu, A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation, Numer. Math. 103 (2006), pp. 393–412. doi: 10.1007/s00211-005-0673-7
   Web of Science ®Google Scholar
• C.-H. Guo, B. Iannazzo and B. Meini, On the doubling algorithm for a (shifted) nonsymmetric algebraic Riccati equations, SIAM J. Matrix Anal. Appl. 29 (2007), pp. 1083–1100. doi: 10.1137/060660837
   Web of Science ®Google Scholar
• N. Huang and C.-F. Ma, Some predictor-corrector-type iterative schemes for solving nonsymmetric algebraic Riccati equations arising in transport theory, Numer. Linear Algebra Appl. 21 (2014), pp. 761–780. doi: 10.1002/nla.1932
   Web of Science ®Google Scholar
• J. Juang, Existence of algebraic matrix Riccati equations arising in transport theory, Linear Algebra Appl. 230 (1995), pp. 89–100. doi: 10.1016/0024-3795(93)00366-8
   Web of Science ®Google Scholar
• J. Juang and I.-D. Chen, Iterative solution for a certain class of algebraic matrix Riccati equations arising in transport theory, Transport Theory Statist. Phys. 22 (1993), pp. 65–80. doi: 10.1080/00411459308203530
   Google Scholar
• J. Juang and Z.-T. Lin, Convergence of an iterative technique for algebraic matrix Riccati equations and applications to transport theory, Transport Theory Stat. Phys. 21 (1992), pp. 87–100. doi: 10.1080/00411459208203523
   Google Scholar
• J. Juang and W.-W. Lin, Nonsymmetric algebraic Riccati equations and Hamiltonian-like matrices, SIAM J. Matrix Anal. Appl. 20 (1998), pp. 228–243. doi: 10.1137/S0895479897318253
   Web of Science ®Google Scholar
• J.-L. Li, T.-Z. Huang and Z.-J. Zhang, The relaxed Newton-like method for a nonsymmetric algebraic Riccati equation, J. Comput. Anal. Appl. 13 (2011), pp. 1132–1142.
   Google Scholar
• J.-L. Li, J.-X. Xue and X.-Y. Li, A note on the relaxed Newton-like method for nonsymmetric algebraic Riccati equation, J. Comput. Anal. Appl. 17 (2014), pp. 574–578.
   Google Scholar
• J.-L. Li, L.-T. Zhang, X.-D. Li and Q.-B. Li, A modified Newton–Shamanskii method for a nonsymmetric algebraic Riccati equation, J. Comput. Anal. Appl. 21 (2016), pp. 380–393.
   Google Scholar
• Y.-Q. Lin, A class of iterative methods for solving nonsymmetric algebraic Riccati equations arising in transport theory, Comput. Math. Appl. 56 (2008), pp. 3046–3051. doi: 10.1016/j.camwa.2008.07.028
   Web of Science ®Google Scholar
• Y.-Q. Lin and L. Bao, Convergence analysis of the Newton–Shamanskii method for a nonsymmetric algebraic Riccati equation, Numer. Linear Algebra Appl. 15 (2008), pp. 535–546. doi: 10.1002/nla.582
   Web of Science ®Google Scholar
• M.-M. Lin and C.-Y. Chiang, The shift techniques for a nonsymmetric algebraic Riccati equation, Appl. Math. Comput. 219 (2013), pp. 5083–5095.
   Web of Science ®Google Scholar
• Y.-Q. Lin, L. Bao and Q. Wu, On the convergence rate of an iterative method for solving nonsymmetric algebraic Riccati equations, Comput. Math. Appl. 62 (2011), pp. 4178–4184. doi: 10.1016/j.camwa.2011.09.068
   Web of Science ®Google Scholar
• L.-Z. Lu, Newton iterations for a non-symmetric algebraic Riccati equation, Numer. Linear Algebra Appl. 12 (2005), pp. 191–200. doi: 10.1002/nla.411
   Web of Science ®Google Scholar
• L.-Z. Lu, Solution form and simple iteration of a nonsymmetric algebraic Riccati equation arising in transport theory, SIAM J. Matrix Anal. Appl. 26 (2005), pp. 679–685. doi: 10.1137/S0895479801397275
   Web of Science ®Google Scholar
• V. Mehrmann and H. Xu, Explicit solutions for a Riccati equation from transport theory, SIAM J. Matrix Anal. Appl. 30 (2008), pp. 1339–1357. doi: 10.1137/070708743
   Web of Science ®Google Scholar
• P. Nelson, Convergence of a certain monotone iteration in the reflection matrix for a nonmultiplying half-space, Transport Theory Stati. Phys. 13 (1984), pp. 97–106. doi: 10.1080/00411458408211655
   Google Scholar
• A. Shimizu and K. Aoki, Application of Invariant Embedding to Reactor Physics, Academic Press, New York, 1972.
   Google Scholar
• X. Wang, W.-W. Lin and L. Dai, On inexact Newton methods based on doubling iteration scheme for symmetric algebraic Riccati equations, J. Comput. Appl. Math. 260 (2014), pp. 364–374. doi: 10.1016/j.cam.2013.09.074
   Web of Science ®Google Scholar
• P.-C.-Y. Weng, H.-Y. Fan and E.-K. Chu, Low-rank approximation to the solution of a nonsymmetric algebraic Riccati equation from transport theory, Appl. Math. Comput. 219 (2012), pp. 729–740. doi: 10.1016/j.camwa.2011.11.031
   Web of Science ®Google Scholar
• S. Wu and C. Huang, Two-step relaxation Newton method for nonsymmetric algebraic Riccati equations arising from transport theory, Math. Probl. Eng. 2009 (2009), Article ID 783920, 17 pages.
   Web of Science ®Google Scholar
• B. Yu and N. Dong, A structure-preserving doubling algorithm for quadratic matrix equations arising from damped mass-spring system, Adv. Model. Optim. 12 (2010), pp. 85–100.
   Google Scholar
• B. Yu, N. Dong, Q. Tang and F.-H. Wen, On iterative methods for the quadratic matrix equation with M-matrix, Appl. Math. Comput. 218 (2011), pp. 3303–3310.
   Web of Science ®Google Scholar
• B. Yu, D.-H. Li and N. Dong, Convergence of the cyclic reduction algorithm for a class of weakly overdamped quadratics, J. Comput. Math. 30 (2012), pp. 139–156. doi: 10.4208/jcm.1110-m3395
   Web of Science ®Google Scholar
• B. Yu, D.-H. Li and N. Dong, Low memory and low complexity iterative schemes for a nonsymmetric algebraic Riccati equation arising from transport theory, J. Comput. Appl. Math. 250 (2013), pp. 175–189. doi: 10.1016/j.cam.2013.03.017
   Web of Science ®Google Scholar