Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SJVM_2007_10_1_a3, author = {M. R. Larin}, title = {On a~modification of algebraic multilevel iteration method for finite element matrices}, journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki}, pages = {61--76}, publisher = {mathdoc}, volume = {10}, number = {1}, year = {2007}, language = {en}, url = {http://geodesic.mathdoc.fr/item/SJVM_2007_10_1_a3/} }
TY - JOUR AU - M. R. Larin TI - On a~modification of algebraic multilevel iteration method for finite element matrices JO - Sibirskij žurnal vyčislitelʹnoj matematiki PY - 2007 SP - 61 EP - 76 VL - 10 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SJVM_2007_10_1_a3/ LA - en ID - SJVM_2007_10_1_a3 ER -
M. R. Larin. On a~modification of algebraic multilevel iteration method for finite element matrices. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 1, pp. 61-76. http://geodesic.mathdoc.fr/item/SJVM_2007_10_1_a3/
[1] Apel T., Anisotropic Finite Elements: Local Estimates and Applications, Advances in Num. Math., Teubner, Stutgart–Leipzig, 1999 | MR | Zbl
[2] Axelsson O., Iterative Solution Methods, Cambridge University Press, New York, 1994 | MR | Zbl
[3] Axelsson O., “The Method of Diagonal Compensation of Reduced Matrix Entries and Multilevel Iteration”, J. Comput. Appl. Math., 83 (1991), 31–43 | DOI | MR
[4] Axelsson O., Barker V. A., Finite Element Solution of Boundary Value Problems: Theory and Computation, Academic Press, Inc., 1984 | MR | Zbl
[5] Axelsson O., Eijkhout V., “The nested recursive two-level factorization method for nine-point difference matrices”, SIAM J. Sci. Stat. Comp., 12 (1991), 1373–1400 | DOI | MR | Zbl
[6] Axelsson O., Larin M., “An algebraic multilevel iteration method for finite element matrices”, J. Comp. Appl. Math., 89 (1997), 135–153 | DOI | MR
[7] Axelsson O., Neytcheva M., “Algebraic multilevel iteration method for Stieltjes matrices”, Numer. Lin. Alg. Appl., 1 (1994), 213–236 | DOI | MR | Zbl
[8] Axelsson O., Padiy A., “On the additive version of the algebraic multilevel iteration method for anisotropic elliptic problems”, SIAM J. Sci. Comput., 20 (1999), 1807–1830 | DOI | MR | Zbl
[9] Axelsson O., Vassilevski P., “Algebraic multilevel preconditioning methods I”, Numer.Math., 56 (1989), 157–177 | DOI | MR | Zbl
[10] Axelsson O., Vassilevski P., “Algebraic multilevel preconditioning methods II”, SIAM J. Numer. Anal., 27 (1990), 1569–1590 | DOI | MR | Zbl
[11] Axelsson O., Vassilevski P., “Variable-step multilevel preconditioning methods, I: Self-adjoint and positive definite elliptic problems”, Numer. Lin. Alg. Appl., 1 (1994), 75–101 | DOI | MR | Zbl
[12] Beauwens R., “Modified incomplete factorization strategies”, Lect. Notes in Math., 1457, 1990, 1–16 | MR | Zbl
[13] Gantmakher F. R., The Theory of Matrices, Chelsea, New York, 1959
[14] Il'in V. P., Iterative Incomplete Factorization Methods, World Scientific Publishing Co., Singapore, 1992 | MR
[15] Larin M., “An algebraic multilevel iterative method of incomplete factorization for Stieltjes matrices”, Comput. Math. Math. Physics, 38 (1998), 1011–1025 | MR | Zbl
[16] Larin M., “An optimal incomplete factorization method for Stieltjes matrices”, Recent advances in numerical methods and applications, eds. O. Iliev etc., World Scientific Publ., Singapore, 1999, 696–704 | MR | Zbl
[17] Larin M., “Using a compensation principle in algebraic multilevel iteration method for finite element matrices”, Siberian J. of Numer. Mathematics / Sib. Branch of Russ. Acad. of Sci., 8:2 (2005), 127–142 | Zbl
[18] Notay Y., “Solving positive (semi)definite linear systems by preconditioned iterative methods”, Lect. Notes in Math., 1457, 1990, 105–125 | MR | Zbl
[19] Notay Y., “DRIC: a dynamic version of the RIC method”, Numer. Lin. Alg. Appl., 1 (1994), 511–532 | DOI | MR | Zbl
[20] Notay Y., “Using approximate inverses in algebraic multilevel methods”, Numer. Math., 80 (1998), 397–417 | DOI | MR | Zbl
[21] Notay Y., “Optimal V cycle algebraic multilevel preconditioning”, Numer. Lin. Alg. Appl., 5 (1998), 441–459 | 3.0.CO;2-J class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl
[22] Notay Y., “Optimal order preconditioning of finite diRerence matrices”, SIAM J. Sci. Comp., 21 (2000), 1991–2007 | DOI | MR | Zbl
[23] Notay Y., “Robust parameter-free algebraic multilevel preconditioning”, Numer. Lin. Alg. Appl., 9 (2002), 409–428 | DOI | MR | Zbl
[24] Vassilevski P., “Hybrid V-cycle algebraic multilevel preconditioners”, Math. Comp., 58 (1992), 489–512 | DOI | MR | Zbl