References
- Balay, S., Abhyankar, S., Adams, M., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Dener, A., Eijkhout, V., Gropp, W. et al. (2022). PETSc users manual, https://petsc.org/release/docs/manual.
- Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F. and Zhang, H. (2001). PETSc, http://www.mcs.anl.gov/petsc.
- Bathe, K.-J. and Wilson, E.L. (1973). Solution methods for eigenvalue problems in structural mechanics, International Journal for Numerical Methods in Engineering 6(2): 213–226.
- Bennighof, J.K. and Lehoucq, R.B. (2004). An automated multilevel substructuring method for eigenspace computation in linear elastodynamics, SIAM Journal on Scientific Computing 25(6): 2084–2106, DOI: 10.1137/S1064827502400650.
- Collignon, T. and Gijzen, M.V. (2010). Two implementations of the preconditioned conjugate gradient method on heterogeneous computing grids, International Journal of Applied Mathematics and Computer Science 20(1): 109–121, DOI: 10.2478/v10006-010-0008-4.
- Duersch, J.A., Shao, M., Yang, C. and Gu, M. (2018). A robust and efficient implementation of LOBPCG, SIAM Journal on Scientific Computing 40(5): C655–C676, DOI: 10.1137/17M1129830.
- Erhel, J. and Frédéric, G. (1997). An Augmented Subspace Conjugate Gradient, PhD thesis, INRIA, Rennes.
- Fan, X., Chen, P., Wu, R. and Xiao, S. (2014). Parallel computing study for the large-scale generalized eigenvalue problems in modal analysis, Science China Physics, Mechanics and Astronomy 57(3): 477–489.
- Feng, Y. and Owen, D. (1996). Conjugate gradient methods for solving the smallest eigenpair of large symmetric eigenvalue problems, International Journal for Numerical Methods in Engineering 39(13): 2209–2229.
- Geng, M. and Sun, S. (2023). Projection improved SPAI preconditioner for FGMRES, Numerical Mathematics: Theory, Methods and Applications 16(4): 1035–1052.
- Guarracino, M., Perla, F. and Zanetti, P. (2006). A parallel block Lanczos algorithm and its implementation for the evaluation of some eigenvalues of large sparse symmetric matrices on multicomputers, International Journal of Applied Mathematics and Computer Science 16(2): 241–249.
- Hernandez, V., Roman, J.E. and Vidal, V. (2003). SLEPc: Scalable Library for Eigenvalue Problem Computations, Lecture Notes in Computer Science 2565: 377–391.
- Hernandez, V., Roman, J.E. and Vidal, V. (2005). SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems, ACM Transactions on Mathematical Software (TOMS) 31(3): 351–362.
- Hetmaniuk, U. and Lehoucq, R. (2006). Basis selection in LOBPCG, Journal of Computational Physics 218(1): 324–332.
- Il’in, V. (2019). Projection methods in Krylov subspaces, Journal of Mathematical Sciences 240(6): 772–782.
- Knyazev, A.V. (2001). Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SIAM Journal on Scientific Computing 23(2): 517–541.
- Knyazev, A.V., Argentati, M.E., Lashuk, I. and Ovtchinnikov, E.E. (2007). Block locally optimal preconditioned eigenvalue xolvers (BLOPEX) in Hypre and PETSc, SIAM Journal on Scientific Computing 29(5): 2224–2239.
- Kolodziej, S.P., Aznaveh, M., Bullock, M., David, J., Davis, T.A., Henderson, M., Hu, Y. and Sandstrom, R. (2019). The suitesparse matrix collection website interface, Journal of Open Source Software 4(35): 1244.
- Kressner, D., Ma, Y. and Shao, M. (2023). A mixed precision LOBPCG algorithm, Numerical Algorithms 94(4): 1653–1671, DOI: 10.1007/s11075-023-01550-9.
- Lanczos, C. (1950). An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, Journal of Research of the National Bureau of Standards 45(4): 255—282.
- Li, Y., Chen, P.Y., Du, T. and Matusik, W. (2023). Learning preconditioners for conjugate gradient PDE solvers, International Conference on Machine Learning, Honolulu, USA, pp. 19425–19439.
- Roman, J.E., Campos, C., Romero, E. and Tomás, A. (2016). SLEPc users manual, Departamento di Sistemas Informàticos y Computación, Universitat Politècnica de València, TR DSIC-II/24/02, Rev 3.
- Saad, Y. (2003). Iterative Methods for Sparse Linear Systems, SIAM, Philadelphia, USA.
- Sleijpen, G.L. and Van der Vorst, H.A. (2000). A Jacobi–Davidson iteration method for linear eigenvalue problems, SIAM Review 42(2): 267–293.
- Stathopoulos, A. and McCombs, J.R. (2010). PRIMME: PReconditioned Iterative MultiMethod Eigensolver: Methods and software description, ACM Transactions on Mathematical Software 37(2): 21:1–21:30.
- Sulaiman, I.M., Kaelo, P., Khalid, R. and Nawawi, M.K.M. (2024). A descent generalized RMIL spectral gradient algorithm for optimization problems, International Journal of Applied Mathematics and Computer Science 34(2): 225–233, DOI: 10.61822/amcs-2024-0016.
- Wu, L., Romero, E. and Stathopoulos, A. (2017). Primme svds: A high-performance preconditioned SVD solver for accurate large-scale computations, SIAM Journal on Scientific Computing 39(5): S248–S271, DOI: 10.1137/16M1082214.
- Yin, J., Voss, H. and Chen, P. (2013). Improving eigenpairs of automated multilevel substructuring with subspace iterations, Computers & Structures 119(1): 115–124.
- Yuan, M., Chen, P., Xiong, S., Li, Y. and Wilson, E.L. (1989). TheWYD method in large eigenvalue problems, Engineering computations 6(1): 49–57.
- Yuan, Y., Sun, S., Chen, P. and Yuan, M. (2021). Adaptive relaxation strategy on basic iterative methods for solving linear systems with single and multiple right-hand sides, Advances in Applied Mathematics and Mechanics 13(2): 378–403.