We introduce a new two-step iteration method for solving large and sparse non-Hermitian positive definite system of linear equations. We analyze the convergence properties of the method and show that under some conditions it is convergent. We extract the preconditioner of proposed method and apply it to expedite the convergence of the flexible version of GMRES method for solving the system. Numerical experiments support the theoretical results and shows that the new method and the corresponding preconditioner are more efficient than the well-known methods and preconditioners in the literature.
Makhdomi, M. , Khojasteh Salkuyeh, D. and Ahmadnasab, M. (2025). A new two-step iteration method for solving non-Hermitian positive definite linear systems. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.68808.3368
MLA
Makhdomi, M. , , Khojasteh Salkuyeh, D. , and Ahmadnasab, M. . "A new two-step iteration method for solving non-Hermitian positive definite linear systems", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.68808.3368
HARVARD
Makhdomi, M., Khojasteh Salkuyeh, D., Ahmadnasab, M. (2025). 'A new two-step iteration method for solving non-Hermitian positive definite linear systems', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.68808.3368
CHICAGO
M. Makhdomi , D. Khojasteh Salkuyeh and M. Ahmadnasab, "A new two-step iteration method for solving non-Hermitian positive definite linear systems," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.68808.3368
VANCOUVER
Makhdomi, M., Khojasteh Salkuyeh, D., Ahmadnasab, M. A new two-step iteration method for solving non-Hermitian positive definite linear systems. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.68808.3368
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