Liu, Chein-Shan; Wang, Fajie; Gu, Yan A Trefftz/MFS mixed-type method to solve the Cauchy problem of the Laplace equation. (English) Zbl 1428.65100 Appl. Math. Lett. 87, 87-92 (2019). Reviewer: Mahmoud Zaky (Giza) MSC: 65N35 65N80 65N20 65F22 35A08 35J15 PDFBibTeX XMLCite \textit{C.-S. Liu} et al., Appl. Math. Lett. 87, 87--92 (2019; Zbl 1428.65100) Full Text: DOI
Liu, Chein-Shan; Chang, Chih-Wen A real-time Lie-group differential algebraic equations method to solve the inverse nonlinear vibration problems. (English) Zbl 1348.65134 Inverse Probl. Sci. Eng. 24, No. 9, 1569-1586 (2016). MSC: 65M32 35R30 65M20 65F22 65L80 PDFBibTeX XMLCite \textit{C.-S. Liu} and \textit{C.-W. Chang}, Inverse Probl. Sci. Eng. 24, No. 9, 1569--1586 (2016; Zbl 1348.65134) Full Text: DOI
Liu, Chein-Shan A double optimal descent algorithm for iteratively solving ill-posed linear inverse problems. (English) Zbl 1336.65064 Inverse Probl. Sci. Eng. 23, No. 1, 38-66 (2015). MSC: 65F22 65F10 35R25 35R30 65M32 65M30 35K05 PDFBibTeX XMLCite \textit{C.-S. Liu}, Inverse Probl. Sci. Eng. 23, No. 1, 38--66 (2015; Zbl 1336.65064) Full Text: DOI
Liu, Chein-Shan A maximal projection solution of ill-posed linear system in a column subspace, better than the least squares solution. (English) Zbl 1367.65060 Comput. Math. Appl. 67, No. 10, 1998-2014 (2014). MSC: 65F22 15A06 PDFBibTeX XMLCite \textit{C.-S. Liu}, Comput. Math. Appl. 67, No. 10, 1998--2014 (2014; Zbl 1367.65060) Full Text: DOI
Liu, Chein-Shan A vector regularization method to solve linear inverse problems. (English) Zbl 1329.65083 Inverse Probl. Sci. Eng. 22, No. 5, 765-786 (2014). MSC: 65F22 PDFBibTeX XMLCite \textit{C.-S. Liu}, Inverse Probl. Sci. Eng. 22, No. 5, 765--786 (2014; Zbl 1329.65083) Full Text: DOI
Liu, Chein-Shan A globally optimal tri-vector method to solve an ill-posed linear system. (English) Zbl 1293.65063 J. Comput. Appl. Math. 260, 18-35 (2014). MSC: 65F22 PDFBibTeX XMLCite \textit{C.-S. Liu}, J. Comput. Appl. Math. 260, 18--35 (2014; Zbl 1293.65063) Full Text: DOI
Liu, Chein-Shan An optimally generalized steepest-descent algorithm for solving ill-posed linear systems. (English) Zbl 1397.65052 J. Appl. Math. 2013, Article ID 154358, 15 p. (2013). MSC: 65F10 65F22 PDFBibTeX XMLCite \textit{C.-S. Liu}, J. Appl. Math. 2013, Article ID 154358, 15 p. (2013; Zbl 1397.65052) Full Text: DOI
Liu, Chein-Shan An optimal preconditioner with an alternate relaxation parameter used to solve ill-posed linear problems. (English) Zbl 1356.65099 CMES, Comput. Model. Eng. Sci. 92, No. 3, 241-269 (2013). MSC: 65F08 65F22 PDFBibTeX XMLCite \textit{C.-S. Liu}, CMES, Comput. Model. Eng. Sci. 92, No. 3, 241--269 (2013; Zbl 1356.65099)
Liu, Chein-Shan A two-side equilibration method to reduce the condition number of an ill-posed linear system. (English) Zbl 1356.65116 CMES, Comput. Model. Eng. Sci. 91, No. 1, 17-42 (2013). MSC: 65F35 65F22 65F08 PDFBibTeX XMLCite \textit{C.-S. Liu}, CMES, Comput. Model. Eng. Sci. 91, No. 1, 17--42 (2013; Zbl 1356.65116) Full Text: DOI
Liu, Chein-Shan An optimal tri-vector iterative algorithm for solving ill-posed linear inverse problems. (English) Zbl 1281.65100 Inverse Probl. Sci. Eng. 21, No. 4, 650-681 (2013). MSC: 65L09 65F22 35J05 35K05 35R30 65N21 65M12 34A34 65N12 PDFBibTeX XMLCite \textit{C.-S. Liu}, Inverse Probl. Sci. Eng. 21, No. 4, 650--681 (2013; Zbl 1281.65100) Full Text: DOI
Liu, Chein-Shan A dynamical Tikhonov regularization for solving ill-posed linear algebraic systems. (English) Zbl 1259.65068 Acta Appl. Math. 123, No. 1, 285-307 (2013). MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{C.-S. Liu}, Acta Appl. Math. 123, No. 1, 285--307 (2013; Zbl 1259.65068) Full Text: DOI
Liu, Chein-Shan; Zhang, Su-Ying; Atluri, Satya N. The Jordan structure of residual dynamics used to solve linear inverse problems. (English) Zbl 1356.65112 CMES, Comput. Model. Eng. Sci. 88, No. 1, 29-48 (2012). MSC: 65F22 15A06 PDFBibTeX XMLCite \textit{C.-S. Liu} et al., CMES, Comput. Model. Eng. Sci. 88, No. 1, 29--48 (2012; Zbl 1356.65112) Full Text: DOI
Liu, Chein-Shan A globally optimal iterative algorithm to solve an ill-posed linear system. (English) Zbl 1356.65102 CMES, Comput. Model. Eng. Sci. 84, No. 4, 383-404 (2012). MSC: 65F10 65F22 PDFBibTeX XMLCite \textit{C.-S. Liu}, CMES, Comput. Model. Eng. Sci. 84, No. 4, 383--404 (2012; Zbl 1356.65102) Full Text: DOI
Liu, Chein-Shan Optimally scaled vector regularization method to solve ill-posed linear problems. (English) Zbl 1259.65067 Appl. Math. Comput. 218, No. 21, 10602-10616 (2012). Reviewer: Constantin Popa (Constanţa) MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{C.-S. Liu}, Appl. Math. Comput. 218, No. 21, 10602--10616 (2012; Zbl 1259.65067) Full Text: DOI Link
Liu, Chein-Shan A revision of relaxed steepest descent method from the dynamics on an invariant manifold. (English) Zbl 1356.65111 CMES, Comput. Model. Eng. Sci. 80, No. 1, 57-86 (2011). MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{C.-S. Liu}, CMES, Comput. Model. Eng. Sci. 80, No. 1, 57--86 (2011; Zbl 1356.65111) Full Text: DOI
Liu, Chein-Shan; Atluri, Satya N. An iterative algorithm for solving a system of nonlinear algebraic equations, \(F(x)=0\), using the system of ODEs with an optimum \(a\) in \(dx/dt=l[aF+(1-a)B^{T}F];~B_{ij}=dF_{i}/dx_{j}\). (English) Zbl 1231.65093 CMES, Comput. Model. Eng. Sci. 73, No. 4, 395-432 (2011). MSC: 65H10 PDFBibTeX XMLCite \textit{C.-S. Liu} and \textit{S. N. Atluri}, CMES, Comput. Model. Eng. Sci. 73, No. 4, 395--432 (2011; Zbl 1231.65093) Full Text: DOI
Liu, Chein-Shan; Hong, Hong-Ki; Atluri, Satya N. Novel algorithms based on the conjugate gradient method for inverting ill-conditioned matrices, and a new regularization method to solve ill-posed linear systems. (English) Zbl 1231.65071 CMES, Comput. Model. Eng. Sci. 60, No. 3, 279-308 (2010). MSC: 65F22 65F10 PDFBibTeX XMLCite \textit{C.-S. Liu} et al., CMES, Comput. Model. Eng. Sci. 60, No. 3, 279--308 (2010; Zbl 1231.65071) Full Text: DOI