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http://dx.doi.org/10.12941/jksiam.2020.24.375

THE INDEFINITE LANCZOS J-BIOTHOGONALIZATION ALGORITHM FOR SOLVING LARGE NON-J-SYMMETRIC LINEAR SYSTEMS  

KAMALVAND, MOJTABA GHASEMI (DEPARTMENT OF MATHEMATICAL SCIENCES, LORESTAN UNIVERSITY)
ASIL, KOBRA NIAZI (DEPARTMENT OF MATHEMATICAL SCIENCES, LORESTAN UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.24, no.4, 2020 , pp. 375-385 More about this Journal
Abstract
In this paper, a special indefinite inner product, named hyperbolic scalar product, is used and all acquired results have been raised and proved with the proviso that the space is equipped with this indefinite scalar product. The main objective is to be introduced and applied an indefinite oblique projection method, called Indefinite Lanczos J-biorthogonalizatiom process, which in addition to building a pair of J-biorthogonal bases for two used Krylov subspaces, leads to the introduction of a process for solving large non-J-symmetric linear systems, i.e., Indefinite two-sided Lanczos Algorithm for Linear systems.
Keywords
Krylov subspace methods; indefinite inner products; Hyperbolic scalar product; non-J-symmetric matrix; J-biorthogonalization; Indefinite Lanczos J-biort-hogonalizatiom Algorithm; Indefinite two-sided Lanczos Algorithm;
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1 R. ONN, A.O. STEINHARDT, A. BOJANCZYK, The hyperbolic singular value decomposition and applications. Applied Mathematics and Computing, Trans. 8th Army Conf., Ithaca-NY (USA)(1990), ARO Rep. 91-1, 93-108, (1991).
2 V. SEGO, The hyperbolic Schur decomposition, Linear Algebra Appl. Linear Algebra Appl., 440 (2014), 90-110.   DOI
3 K. N. ASIL AND M. G. KAMALVAND, Some hyperbolic iterative methods for linear systems, Journal of Applied Mathematics, vol. 2020, Article ID 9874162, 8 pages, 2020.
4 M. G. KAMALVAND AND K. N. ASIL, Indefinite Ruhe's Variant of the Block Lanczos Method for Solving the Systems of Linear Equations, Advances in Mathematical Physics, Volume 2020, Article ID 2439801, 9 pages.
5 C. LANCZOS, Solution of systems of linear equations by minimized iteration. J. Res. Nat. Bureau Standards. 49 (1952), 33-53.   DOI
6 I.GOHBERG, P.LANCASTER, L.RODMAN, Indefinite linear algebra and applications. Birkhauser, 2005.
7 Y. SAAD, Iterative methods for sparse linear systems. Industrial and Applied Mathematics, 3600 University City Science Center Philadelphia, PA. United States, 2003.
8 Y. SAAD, Numerical methods for large eigenvalueproblems. Second edition, 2011.
9 N.J. HIGHAM, J-orthogonal matrices: properties and generations. SIAM, Rev. 45(3):504-519, (2003).   DOI
10 A. KIHCMAN, Z.A. ZHOUR, The representation and approximation for the weighted Minkowski inverse in Minkowski space. Math. Comput. Modelling, 47(3-4):363-371,(2008).   DOI
11 B.C. LEVY, A note on the hyperbolic singular value decomposition. Linear Algebra Appl., 277(1-3):135-142, (1998).   DOI