F. P. A. Beik and M. Benzi, Preconditioning techniques for the coupled Stokes-Darcy problem: spectral and field-of-values analysis, Numerische Mathematik, 150 (2022) 257-298.
F. P. A. Beik, M. Najafi-Kalyani and K. Jbilou, Preconditioned iterative methods for multi-linear systems based on the majorization matrix, Linear and Multilinear Algebra, 70 (2022) 5827-5846.
F. P. A. Beik, El Ichi , K. Jbilou and R. Sadaka, Tensor extrapolation methods with applications, Numerical Algorithms, 87 (2021), 1421-1444.
F. P. A. Beik, K. Jbilou, M. Najafi-Kalyani and L. Reichel, On the Golub-Kahan bidiagonalization for ill-posed tensor equations with applications to color image restoration, Numerical Algorithms, 84 (2020), 1535-1563.
F. P. A. Beik, M. Najafi-Kalyani and L. Reichel, Iterative Tikhonov regularization of tensor equations based on the Arnoldi process and some of its generalizations, Applied Numerical Mathematics, 151 (2020), 425--447.
M. Najafi-Kalyani, F. P. A. Beik andK. Jbilou, On global iterative schemes based on Hessenberg process for (ill-posed) Sylvester tensor equations, Journal of Computational and Applied Mathematics, 373 (2020) 112216.
F. P. A. Beik and M. Benzi,Block preconditioners for saddle point systems arising from liquid crystal directors modeling, CALCOLO,(2018) 55: 29.
F. P. A. Beik and M. Benzi, Iterative methods for double saddle point systems, SIAM Journal on Matrix Analysis and Applications.39 (2018), no. 2, 902–921.
F. P. A. Beik, M. Benzi and S.-H. A. Chaparpordi, On block diagonal and block triangular iterative schemes and preconditioners for stabilized saddle point problems, Journal of Computational and Applied Mathematics,326 (2017), 15-30.
F. P. A. Beik, F. S. Movahed and S. Ahmadi-Asl, On the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations, Numerical Linear Algebra with Applications,23 (2016), no. 3, 444-466.
Other Publications
F. P. A. Beik, M. Najafi-Kalyani and S. Mollahasani, On the solvability of tensor absolute value equations, Bulletin of the Malaysian Mathematical Sciences Society, 45 (2022), 3157- 3176.
M. Najafi-Kalyani and F. P. A. Beik, An optimality property of approximated solution computed by Hessenberg method, Mathematical Communications, 27 (2022), 223-237.
M. E Guide, El Ichi , K. Jbilou and F. P. A. Beik, Tensor Krylov subspace methods via the Einstein product with applications to image and video processing, Applied Numerical Mathematics, 181 (2022) 347-363.
S. Mollahasani and F. P. A. Beik, Absolute value equations with tensor product structure: unique solvability and numerical solution, Applications of Mathematics, 67 (2022) 657-674.
N. N. Shams and F. P. A. Beik, An improvement on a class of fixed point iterative methods for solving absolute value equations, Computational Methods in Applied Mathematics, 22 (2022) 663-673.
H. Aslani, D. K. Salkuyeh. and F. P. A. Beik, On the preconditioning of three-by-three block saddle point problems, FILOMAT, 35 (2021), 5181-5194.
F. P. A. Beik and M. Najafi-Kalyani, A preconditioning technique in conjunction with Krylov subspace methods for solving multilinear systems, Applied Mathematics Letters, 116 (2021) 107051.
M. Najafi-Kalyani and F. P. A. Beik, A preconditioned Jacobi-type method for solving multi-linear systems, The Journal of Mahani Mathematical Research Center, 10 (2) 21-31.
A. Ameri and F. P. A. Beik, Note to the convergence of minimum residual HSS method, Journal of Mathematical Modeling, 9 (2021) 323--330.
N. N. Shams, A. Fakharzadeh J. and F. P. A. Beik, Iterative schemes induced by block splittings for solving absolute value equations, FILOMAT, 34 (2020), no. 12,4171-4188.
M. Benzi, F. P. A. Beik, S.-H. A. Chaparpordi and Z. Roygar, Generalized iterative methods for solving double saddle point problem, Mathematical Researches.5 (2020), no. 2, 137-150. (In Persian).
S.-H. A. Chaparpordi, F. P. A. Beik and D. K. Salkuyeh,Block triangular preconditioners for stabilized saddle point problems with nonsymmetric $(1,1)$-block, Computers & Mathematics with Applications. 76 (2018), no. 6, 1544-1553.
M. Benzi and F. P. A. Beik, Uzawa-type and augmented Lagrangian methods for double saddle point systems, Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, Springer, Cham, 2019, 215-236.
A. Ameri and F. P. A. Beik, Delayed over-relaxation in iterative schemes to solve rank deficient linear systems of (matrix) equations, FILOMAT, 32 (2018), no. 9, 3181-3198.
F. P. A. Beik, S. Ahmadi-Asl and A. Ameri, On the iterative refinement of the solution of ill-conditioned linear system of equations, International Journal of Computer Mathematics,95 (2018), no. 2, 427-443.
S. Ahmadi-Asl and F. P. A. Beik, An efficient iterative algorithm for quaternionic least-squares problems over the generalized $eta$-(anti-)bi-Hermitian matrices, Linear and Multilinear Algebra, 65 (2017), no. 9, 1743-1769.
F. P. A. Beik and D.K. Salkuyeh, A cyclic iterative approach and its modified version to solve coupled Sylvester-transpose matrix equations, Linear and Multilinear Algebra, 65 (2017), no. 12, 2406-2423.
S. Ahmadi-Asl and F. P. A. Beik, Iterative algorithms for least-squares solutions of a quaternion matrix equation, Journal of Applied Mathematics and Computing,53 (2017), no. 1, 95-127.
F. P. A. Beik and D.K. Salkuyeh, An iterative algorithm for the best approximate $(P,Q)$-orthogonal symmetric and skew-symmetric solution pair of coupled matrix equations, Transactions of the Institute of Measurement and Control, 39 (2017), no. 4, 537-554.
D. K. Salkuyeh, M. Hasani and F. P. A. Beik, On the preconditioned AOR iterative method for Z-matrices, Computational & Applied Mathematics, 36 (2017), 877-883.
D. K. Salkuyeh, F. P. A. Beik, D. Hezari, A sequential two-stage method for solving generalized saddlepoint problems, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics,79 (2017), no. 1, 131-140.
F. P. A. Beik, On a general class of preconditioners for nonsymmetric generalized saddle point problems, U.P.B. Sci. Bull., Series A: Applied Mathematics and Physics, 78 (2016), no. 4, 211-220.
F. P. A. Beik and S. Ahmadi-Asl, An iterative algorithm for $eta$-(anti)-Hermitian least-squares solutions of quaternion matrix equations, Electronic Journal of Linear Algebra (ELA), 30 (2015) 372-401.
F. P. A. Beik and N. N. Shams, On the modified iterative methods for M-matrix linear system, Bulletin of the Iranian Mathematical Society (BIMS), 41 (2015), no. 6, 1519-1535.
F. P. A. Beik and D.K. Salkuyeh, An iterative algorithm for the least squares solutions of matrix equations over symmetric arrowhead matrices, Journal of the Korean Mathematical Society, 52 (2015) 349-372.
F. P. A. Beik and D.K. Salkuyeh, Weighted versions of Gl-FOM and Gl-GMRES for solving general coupled linear matrix equations, Computational Mathematics and Mathematical Physics, 55 (2015), no. 10, 1606-1618.
D. K. Salkuyeh and F. P. A. Beik, Minimum norm least-squares solution to general complex coupled linear matrix equations via iteration, FILOMAT, 29 (2015) 1389-1407.
F. P. A. Beik and S. Ahmadi-Asl, Residual norm steepest descent based iterative algorithms for Sylvester tensor equations, Journal of Mathematical Modeling, 2 (2015) 115-131.
F. P. A. Beik and D.K. Salkuyeh, A finite iterative algorithm for Hermitian reflexive and skew-Hermitian solution groups of the general coupled linear matrix equations, Journal of Applied Mathematics and Computing,48 (2015) 129-155.
F. P. A. Beik and N. N. Shams, Preconditioned generalized mixed-type splitting iterative method for solving weighted least squares problems, International Journal of Computer Mathematics, 91 (2014), no. 5, 944–963.
F. P. A. Beik, A modified iterative algorithm for the (Hermitian) reflexive solution of the generalized Sylvester matrix equation, Transactions of the Institute of Measurement and Control,36 (2014), no. 6, 815–827.
F. P. A. Beik and M. M. Moghadam, The general coupled linear matrix equations with conjugate and transpose unknowns over the mixed groups of generalized reflexive and anti-reflexive matrices, Computational & Applied Mathematics, 33 (2014) 795–820.
D. K. Salkuyeh and F. P. A. Beik, On the gradient based algorithm for solving the general coupled matrix equations, Transactions of the Institute of Measurement and Control,36 (2014), no. 3, 375-381.
F. P. A. Beik, D.K. Salkuyeh and M. M. Moghadam, Gradient based iterative algorithm for solving the generalized coupled Sylvester-transpose and conjugate matrix equations over reflexive (anti-reflexive) matrices, Transactions of the Institute of Measurement and Control, 36 (2014), no. 1, 99-110.
D.K. Salkuyeh and F. P. A. Beik, An iterative method to solve symmetric positive definite matrix equations, Mathematical Reports, 16 (2014), no. 2, 271-283.
F. P . A. Beik, Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations, Bulletin of the Iranian Mathematical Society (BIMS), 40 (2014) 1097-1117.
F. P. A. Beik and D.K. Salkuyeh, The coupled Sylvester-transpose matrix equations over generalized centro-symmetric matrices, International Journal of Computer Mathematics, 90 (2013), no. 7, 1546-1566.
M. M. Moghadam and F. P. A. Beik, Comparison results on the preconditioned mixed-type splitting iterative method for M-matrix linear systems, Bulletin of the Iranian Mathematical Society (BIMS), 38 (2012), no. 2, 349-367.
F. P. A. Beik and D.K. Salkuyeh, On the global Krylov subspace methods for solving general coupled matrix equations, Computers & Mathematics with Applications, 62 (2011), no. 11, 4605-4613.
List of selected papers
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