Apushkinskiy, E. G.; Kozhevnikov, V. A.; Biryukov, A. V. Comparison of approximate and numerical methods for solving the homogeneous Dirichlet problem for the Helmholtz operator in a two-dimensional domain. (English) Zbl 07792264 Lobachevskii J. Math. 44, No. 9, 3989-3997 (2023). MSC: 65N35 65N30 65N06 35J05 35J25 35B38 33C10 78A60 35Q60 PDFBibTeX XMLCite \textit{E. G. Apushkinskiy} et al., Lobachevskii J. Math. 44, No. 9, 3989--3997 (2023; Zbl 07792264) Full Text: DOI
Helsing, Johan; Jiang, Shidong Solving Fredholm second-kind integral equations with singular right-hand sides on non-smooth boundaries. (English) Zbl 07516798 J. Comput. Phys. 448, Article ID 110714, 16 p. (2022). MSC: 65Nxx 15Axx 35Jxx PDFBibTeX XMLCite \textit{J. Helsing} and \textit{S. Jiang}, J. Comput. Phys. 448, Article ID 110714, 16 p. (2022; Zbl 07516798) Full Text: DOI arXiv
Zhang, Li-Ping; Li, Zi-Cai; Huang, Hung-Tsai; Lee, Ming-Gong Comparisons of method of fundamental solutions, method of particular solutions and the MFS-QR; stability analysis. (English) Zbl 1464.65277 Eng. Anal. Bound. Elem. 123, 182-199 (2021). MSC: 65N80 65N12 PDFBibTeX XMLCite \textit{L.-P. Zhang} et al., Eng. Anal. Bound. Elem. 123, 182--199 (2021; Zbl 1464.65277) Full Text: DOI
Bachmayr, Markus; Kazeev, Vladimir Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs. (English) Zbl 1454.65160 Found. Comput. Math. 20, No. 5, 1175-1236 (2020). MSC: 65N30 65N55 65N12 65F08 65F10 65F35 65Y20 15A69 35J25 PDFBibTeX XMLCite \textit{M. Bachmayr} and \textit{V. Kazeev}, Found. Comput. Math. 20, No. 5, 1175--1236 (2020; Zbl 1454.65160) Full Text: DOI arXiv
Kamenski, Lennard; Huang, Weizhang; Xu, Hongguo Conditioning of finite element equations with arbitrary anisotropic meshes. (English) Zbl 1303.65097 Math. Comput. 83, No. 289, 2187-2211 (2014). Reviewer: Ivan Secrieru (Chişinău) MSC: 65N30 65F35 35J25 65N50 PDFBibTeX XMLCite \textit{L. Kamenski} et al., Math. Comput. 83, No. 289, 2187--2211 (2014; Zbl 1303.65097) Full Text: DOI arXiv
Li, Zi-Cai; Huang, Hung-Tsai; Wei, Yimin Ill-conditioning of the truncated singular value decomposition, Tikhonov regularization and their applications to numerical partial differential equations. (English) Zbl 1249.65087 Numer. Linear Algebra Appl. 18, No. 2, 205-221 (2011). Reviewer: Martin Plešinger (Liberec) MSC: 65F22 35J05 35J25 65N20 65F20 65F35 65N35 PDFBibTeX XMLCite \textit{Z.-C. Li} et al., Numer. Linear Algebra Appl. 18, No. 2, 205--221 (2011; Zbl 1249.65087) Full Text: DOI
Jiránek, Pavel; Strakoš, Zdeněk; Vohralík, Martin A posteriori error estimates including algebraic error and stopping criteria for iterative solvers. (English) Zbl 1215.65168 SIAM J. Sci. Comput. 32, No. 3, 1567-1590 (2010). Reviewer: Adrian Carabineanu (Bucureşti) MSC: 65N15 65F10 65N08 35J25 65N50 PDFBibTeX XMLCite \textit{P. Jiránek} et al., SIAM J. Sci. Comput. 32, No. 3, 1567--1590 (2010; Zbl 1215.65168) Full Text: DOI
Atkinson, Kendall; Han, Weimin Theoretical numerical analysis. A functional analysis framework. 3rd ed. (English) Zbl 1181.47078 Texts in Applied Mathematics 39. Berlin: Springer (ISBN 978-1-4419-0457-7/hbk; 978-1-4419-0458-4/ebook). xvi, 625 p. (2009). Reviewer: Costică Moroşanu (Iaşi) MSC: 47N40 46N40 65-01 65N12 65D05 65Jxx 65R20 PDFBibTeX XMLCite \textit{K. Atkinson} and \textit{W. Han}, Theoretical numerical analysis. A functional analysis framework. 3rd ed. Berlin: Springer (2009; Zbl 1181.47078) Full Text: DOI
Bebendorf, M. Hierarchical LU decomposition-based preconditioners for BEM. (English) Zbl 1071.65031 Computing 74, No. 3, 225-247 (2005). MSC: 65F05 65F35 65F50 65N38 35J40 PDFBibTeX XMLCite \textit{M. Bebendorf}, Computing 74, No. 3, 225--247 (2005; Zbl 1071.65031) Full Text: DOI
Arioli, M.; Loghin, D.; Wathen, A. J. Stopping criteria for iterations in finite element methods. (English) Zbl 1069.65124 Numer. Math. 99, No. 3, 381-410 (2005). Reviewer: Dinh Nho Hao (Brussels) MSC: 65N30 65F10 65F35 35J25 65N12 PDFBibTeX XMLCite \textit{M. Arioli} et al., Numer. Math. 99, No. 3, 381--410 (2005; Zbl 1069.65124) Full Text: DOI Link
Arioli, M. A stopping criterion for the conjugate gradient algorithm in a finite element method framework. (English) Zbl 1048.65029 Numer. Math. 97, No. 1, 1-24 (2004). MSC: 65F10 35J25 65N30 65F35 PDFBibTeX XMLCite \textit{M. Arioli}, Numer. Math. 97, No. 1, 1--24 (2004; Zbl 1048.65029) Full Text: DOI Link
Hoteit, H.; Erhel, J.; Mosé, R.; Philippe, B.; Ackerer, Ph. Numerical reliability for mixed methods applied to flow problems in porous media. (English) Zbl 1079.76581 Comput. Geosci. 6, No. 2, 161-194 (2002). MSC: 76M10 65M60 65N30 76S05 PDFBibTeX XMLCite \textit{H. Hoteit} et al., Comput. Geosci. 6, No. 2, 161--194 (2002; Zbl 1079.76581) Full Text: DOI
Bhuruth, M.; Jain, M. K.; Gopaul, A. Preconditioned iterative methods for the nine-point approximation to the convection-diffusion equation. (English) Zbl 0993.65117 J. Comput. Appl. Math. 138, No. 1, 73-92 (2002). MSC: 65N06 65F10 65F35 35J25 65N12 PDFBibTeX XMLCite \textit{M. Bhuruth} et al., J. Comput. Appl. Math. 138, No. 1, 73--92 (2002; Zbl 0993.65117) Full Text: DOI
Brown, B. M.; Jimack, P. K.; Mihajlović, M. D. An efficient direct solver for a class of mixed finite element problems. (English) Zbl 0982.65119 Appl. Numer. Math. 38, No. 1-2, 1-20 (2001). MSC: 65N25 65N30 65Y05 65Y20 35J40 35P15 65F05 PDFBibTeX XMLCite \textit{B. M. Brown} et al., Appl. Numer. Math. 38, No. 1--2, 1--20 (2001; Zbl 0982.65119) Full Text: DOI