Dr. Davod Khojasteh Salkuyeh
Faculty: Faculty of Mathematical Sciences
Department: Department of Applied Mathematics
University of Guilan
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Dr. Davod Khojasteh Salkuyeh

Academic Rank: Professor

Faculty: Faculty of Mathematical Sciences

Department: Department of Applied Mathematics

Profile :: Education :: Publications :: Courses :: Schedule :: CV :: Contact

I was born in Salkuyeh (a very nice village in Langarud, Guilan province, Iran) in 1970. I graduated from Ghoddosi high school of Langarud in 1989. I received my B.Sc degree in applied mathematics in 1994 from Sharif university of technology, Tehran, Iran and M.Sc degree in applied mathematics in 1997 from Ferdowsi university of Mashhad, Iran. I wrote my dissertation under supervision of Prof. Asghar Kerayechian. I received my Ph.D degree under supervision of professor Faezeh Toutounian at Ferdowsi University of Mashhad in May 4, 2003. Then, I joined Mohaghegh Ardabili University of Ardabil, Iran. From February 2012, I have joined the Faculty of Mathematical Sciences, University of Guilan. My research interests are mainly iterative methods and preconditioning for solving large sparse linear system of equations, finite element and finite difference methods and error analysis.

Honors and Executive Profile:

1. Head of the department of mathematics of University of Mohaghegh Ardabili for two years.
2. Outstanding researcher of the Faculty of Basic Sciences, University of Mohaghegh Ardabili, 2006.
3. Outstanding researcher of the Faculty of Basic Sciences, University of Mohaghegh Ardabili, 2008.
4. Ranked number one among the MSc graduate students, Ferdowsi University of Mashhad, 1997.
5. Outstanding researcher in Basic Sciences of the Ardabil province, 2010.
6. Member of scientific committee of the 4th national mathematics conference, Payameh Noor, Sep. 25 and 26, Ardabil.
7. Invited speaker at the 42nd Annual Iranian Mathematics Conference at Vali-e-Asr University of Rafsanjan, Iran.
8. Member of scientific committee of 5th conference on Numerical Analysis and its Applications, Vali-Asr university, Rafsanjan, 2014.
9. Member of the Board of Trustees Professor Mehdi Radjabalipour Prize"s from 2013.
10. Member of scientific committee of 8th National Mathematics Conference, Payane-Nor university, 2016.
11. Member of scientific committee of 6th conference on Numerical Analysis and its Application, Maragheh university, 2016.
12. Member of scientific committee of 7th conference on Numerical Analysis and its Application, University of Kerman, 2018.
13. Member of scientific committee of 49th Annual Iranian Mathematics Conference at Iran University of Science & Technology, Iran (2018).

Referee for international journals:

1. Journal of Computational and Applied Mathematics
2. Computers Mathematics with Applications
3. International Journal of Computer Mathematics
4. Journal of Applied Mathmatics and Computing
5. Applied Mathematics and Computation
6. Applications and Applied Mathematics
7. Journal of advanced reserach in applied mathematics
8. Computer Physics Communications
9. SDU Journal of Science (E-Journal)
10. World applied science journal.
11. Mathematical and Computer Modelling
12. Journal of Advanced Research in Scientific Computing
13. International Journal of Nonlinear Sciences and Numerical Simulation.
14. Journal of Applied Mathematics
15. Soft Computing-A Fusion of Foundations, Methodologies and Applications.
16. Bulletin of Iranian Mathematical Society.
17. Journal of Intelligent and Fuzzy Systems.
18. Mathematical Modelling and Analysis.
19. Mathematical Problems in Engineering.
20. Applied Mathematical Modelling.
21. Fuzzy Sets and Systems.
22. Optimization Letters.
23. Afrika Matematika.
24. Applied Mathematics Letters.
25. Ain Shams Engineering Journal.
26. Linear and Multilinear Algebra
27. Computational and Applied Mathematics
28. SpringerPlus
30. BIT Numerical Mathematics
31. Wavelet and Linear Algebra


1) Journal of Mathematical Modelling (Published by University of Guilan)

Editorial Boards:

1) Bulletin of Iranian Mathematical Society (BIMS) (2013-2019)
2) Journal of Hyperstructures
3) Iranian Journal of Numerical Analysis and Optimization 
4) Control and Optimization in Applied Mathematics -COAM.
Google Scholar Profile 

Ph.D, Applied Mathematics (Numerical Linear Algebra)

Ferdowsi university of Mashhad, 2004/3/10

Thesis: Some developments on the iterative methods for solving large sparse linear system of equations

Supervisor: Prof. Faezeh Toutounian

 M.Sc, Applied Mathematics (Numerical methods for partial differential equations)

Ferdowsi university of Mashhad Applied Mathmatics 1997/7/11

Dissertation: Solving the Stokes problem by the finite element method

Supervisor: Prof. Asghar Kerayechian


B.Sc, Applied Mathematics (Operational research)

Sharif University of Technology, Applied Mathematics 1995/1/1

Journal papers: 


T.S. Siahkolaei, D.K. Salkuyeh, On the parameter selection in the transformed matrix iteration method, Numer. Algor., Accepted for publication, January 20, 2020. 

D. Khojasteh Salkuyeh, M. Rahimian, Spectral analysis of the MGSS preconditioner for singular saddle point problems,  J. Appl. Math. & Informatics,  38 (2020) 175 - 187.

 D. Khojasteh Salkuyeh, Shifted skew-symmetric/skew-symmetric splitting method and its application to generalized saddle point problems, Applied Mathematics Letters, 103 (2020) 106184..

M. Masoudi, D. Khojasteh Salkuyeh, An extension of the positive-definite and skew-Hermitian splitting method for preconditioning of generalized saddle point problems, Computers & Mathematics with Applications, Published online,

M. Bastani, D. Khojasteh Salkuyeh, On the GSOR iteration method for image restoration,  Numerical Algebra, Control and Optimization, Accepted for publication, September 5, 2019.

T. Salimi Siahkolaei, D. Khojasteh Salkuyeh, A new double-step method for solving complex Helmholtz equation, Hacettepe Journal of Mathematics & Statistics, Accepted for publication, November 13,  2019.

T. Salimi Siahkolaei, D.K. Salkuyeh, On TTSCSP-based iteration methods for complex weakly nonlinear systems, East Asian Journal on Applied Mathematics, 10 (2020) 1-21.

H. Mirchi, D. K. Salkuyeh, A new preconditioner for elliptic PDE-constrained optimization problems, Numerical Algorithms, 83 (2020) 653–668.

M. Jozi, S. Karimi, D. K. Salkuyeh, An Iterative Method to Compute Minimum norm Solutions of Ill-posed Problems in Hilbert Spaces, Afrika Matematika,  30 (2019) 797–816.

 ► O. Axelsson and D.K. Salkuyeh, A new version of a preconditioning method for certain two-by-two block matrices with square blocks, BIT Numerical Mathematics,  59 (2019) 321–342

M. Keyanpour, D.K. Salkuyeh, H. Moosaei and S. Ketabchi, On the solution of the fully fuzzy Sylvester matrix equation,
International Journal of Modelling and Simulation,  40 (2020) 80-85.

 T. Salimi Siahkolaei, D.K. Salkuyeh, A preconditioned SSOR iteration method for solving complex symmetric system of linear equations,
Numerical Algebra, Control and Optimization,  9 (2019) 483-492.

D.K. Salkuyeh and T. Salimi Siahkolaei, Two-parameter TSCSP method for solving complex symmetric system of linear equations,
Calcolo 55 (2018) 8.

S.H. Azizi Chaparpordi, F. Panjeh Ali Beik, D.K. Salkuyeh, Block triangular preconditioners for stabilized saddle point problems with nonsymmetric (1,1)-block,
Computers & Mathematics with Applications, 76 (2018) 1544-1553.

 D.K. Salkuyeh, M. Abdolmaleki, S. Karimi, On a splitting preconditioner for saddle point problems,
Journal of Applied Mathematics & informatics 36 (2018) 459-474.

 D.K. Salkuyeh and F. Panjeh Ali Beik, An explicit formula for the inverse of arrowhead and doubly arrow matrices, 
International Journal of  Applied and Computational Mathematics, 4 (2018) 96.

 M. Pourbagher, D.K. Salkuyeh, On the solution of a class of complex symmetric linear systems,
Applied Mathematics Letters, 76 (2018) 14-20.

D.K. Salkuyeh, M. Rahimian, A modification of the generalized shift-splitting method for singular saddle point problems,
Computers andMathematics with Applications, 74 (2017) 2940-2949.

D. Hezari, V. Edalatpour, H. Feyzollahzadeh, D. K Salkuyeh, On the generalized deteriorated positive semi-definite and skew-Hermitian splitting preconditioner, J. Comput. Math. 37 (2019) 18-32.

M. Bastani, D.K. Salkuyeh, On the m-step two-parameter generalized Hermitian  and skew-Hermitian splitting preconditioning method, Afrika Matematika, 28 (2017) 999-1010.


F. P. A. Beik, D. Khojasteh Salkuyeh, A cyclic iterative approach and its modified version to solve coupled Sylvester-transpose matrix equations,Linear and Multilinear Algebra, 65 (2017) 2406-2423.

V. Edalatpour, D. Hezari and D. Khojasteh Salkuyeh, A generalization of the Gauss-Seidel iteration method for solving absolute value equations, Appl. Math. Comput. 293 (2017) 156-167.

  D. Khojasteh Salkuyeh and  M. Masoudi, A new relaxed HSS preconditioner for saddle point problems,  Numerical Algorithms 74 (2017) 781–795. 

 ► D. Khojasteh Salkuyeh, M. Bastani, A new generalization of the HSS method for solving the continuous Sylvester equation, Transactions of the Institute of Measurement and Control, 40 (2018) 303-317.

  D. Khojasteh Salkuyeh, F. Panjeh Ali Beik, D. Hezari, A sequential two-stage method for solving generalized saddle  point problems,  UPB Scientific Bulletin: Series A Applied Mathematics and Physics, 79 (2017) 131-140 .

 D. Hezari, D. Khojasteh Salkuyeh, V. Edalatpour, A new iterative method for solving a class of complex symmetric system of linear equations, Numerical Algorithms, 73 (2016) 927–955.

D. Khojasteh Salkuyeh, Stepsize Control for Cubic Spline Interpolation,International Journal of Applied and  Computational  Mathematics,  3 (2017) 693–702.

 ► D. Khojasteh Salkuyeh, A. Tavakoli, Interpolated variational iteration method for initial value problems, Applied  Mathematical Modeling, 40 (2016) 3979-3990.

  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 theInstitute of Measurement and Control39 (2017) 537–554.

D.K. Salkuyeh, M. Hasani and F.P.A Beik, On the Preconditioned AOR Iterative Method for Z-Matrices, Computational and Applied Mathematics, 36 (2017) pp 877–883.

 ► V. Edalatpour, D. Hezari and D. Khojasteh Salkuyeh, Two efficient inexact algorithms for a class of large sparse complex linear systems, Mediterranean Journal of Mathematics,  13 (2016) 2301–2318.

 ► D. Hezari, V. Edalatpour and D. Khojasteh Salkuyeh, Preconditioned GSOR iterative method for a class of  complex symmetric system of linear equations, Numerical Linear Algebra with Applications,  2015 (22) 761-776.

  D.K. Salkuyeh, M. Masoudi, D. Hezari, On the generalized shift-splitting preconditioner for saddle point problems, Applied Mathematics Letters, 48 (2015) 55-61.


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 Korean Mathematical Society,   52 (2015) 349—372.

N. Aghazadeh, D.K. Salkuyeh, M. Bastani, Two-parameter generalized Hermitian and skew-Hermitian splitting iteration method, Interational Journal of Computer Mathematics, 93 (2016) 1119–1139.

N. Aghazadeh, M. Bastani, D. K. Salkuyeh, The generalized Hermitian and skew-Hermitian splitting iterative method for image restoration, Applied Mathematical Modelling,  39 (2015) 6126-6138.

 ► A. Golbabai, S.P.A  Beik, D. K. Salkuyeh, A new approach for solving the first-order linear matrix differential equations, Bulletin of Iranian Mathematical Society (BIMS), 42 (2016) 297-314.

V. Edalatpour, D. Hezari and D. K. Salkuyeh,  Accelerated generalized SOR method for a class of complex systems of linear equations, Mathematical Communications, 20 (2015) 37-52.

D.K. Salkuyeh, On the solution of a class of fuzzy system of linear equations, Sadhana, 40 (2015) 369-377. 

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) 1606-1618.

 D. K. Salkuyeh and Z. Hassanzadeh, A Newton two-stage waveform relaxation method for solving systems of nonlinear algebraic equations, Mathematical Communications, 20 (2015) 1-15.


 D. K. Salkuyeh, F. P. A. Beik, Minimum norm least-squares solution to general complex coupled linear matrix equations via iteration, FILOMAT,  29 (2015) 1389-1407.

F. Toutounian, D. K. Salkuyeh, M. Mojarrab, LSMR iterative method for general coupled matrix equations, Journal of Applied Mathematics, 8, 2014.

F.P.A. Beik, 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.


D. K. Salkuyeh, A. Rafiei, H. Roohani, ILU Preconditioning Based on the FAPINV Algorithm, Opuscula Mathematica, 35 (2014) 235–250.

 D. K. Salkuyeh,  V. Edalatpour,  D. Hezari,  Polynomial preconditioning for the GeneRank problem,  Electronic Transactionson Numerical Analysis (ETNA),  41 (2014) 179-189.

D. K. Salkuyeh, D. Hezari, V. Edalatpour, Generalized SOR iterative method for a class of complex symmetric linear system of equations, International Journal of Computer Mathematics,  92 (2015) 802-815.


 D. K. Salkuyeh, The Picard-HSS iteration method for absolute value equations, Optimization Letters,  8 (2014) 2191–2202. 

Z. Hassanzadeh and D.K Salkuyeh, Two-stage waveform relaxation method for the initial value problems with non-constant  coefficients, Computational & Applied Mathematics33 (2014) 641–654. 

  M. Hassani, D. K. Salkuyeh, On a class of multi-level preconditioners for Z-matrices, Afrika Matematika, 26 (2015) 201-213. 

D. K. Salkuyeh, 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 (3) (2014) 375–381.


 S. Erfani, A. Tavakoli, D.K. Salkuyeh, An efficient method to set up a Lanczos based preconditioner for discrete ill-posed problems, Applied Mathematical Modelling, 37 (2013) 8742–8756.

 M. Hasani, D.k. Salkuyeh, Improvements of Two Preconditioned AOR Iterative Methods for Z-Matrices, Bulletin of the IranianMathematical Society (BIMS) 40 (2014) 357-371. 

 F.P.A. Beik,  D.K. Salkuyeh, M. Mohseni 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 ofMeasurement and Control, 36 (2014) 99-110. 

 D.K. Salkuyeh, F.P.A. Beik, An iterative method to solve symmetric positive definite matrix equations,  Mathematical Reports 16 (2014) 271-283.

F. Panjeh Ali Beik and D.K. Salkuyeh, The coupled Sylvester-transpose matrix equations over generalized  centro-symmetric matrices, International Journal of Computer Mathematics,  90 (2013) 1546-1566 .

D. K. Salkuyeh, S. Shamsi, A. Sadeghi, An improved symmetric SOR iterative method for augmented systems, Tamkang J. Mathematics, 43 (2012) 479-490. 

► D.K. Salkuyeh, M. Bastani, Solution of the Complex Modified Korteweg-de Vries Equation by the Projected Differential  Transform Method, Applied Mathematics and Computation,  219 (2013) 5105-5112 .

D.k. Salkuyeh,  An Iterative Method for Symmetric Positive Semidefinite Linear System of Equations, Demonstratio  Mathematica, 47 (2014) 482-492.

 F. Panjeh Ali Beik and D.K. Salkuyeh, On the global Krylov subspace methods for solving general coupled matrix equations, Computers and Mathematics with Applications, 62 (2011) 4605-4613.

M. Bastani and D. K. Salkuyeh, A highly accurate method to solve Fisher"s equation, Pramana-Journal of Physics, 78 (2011) 335-346.

 D. K. Salkuyeh and S. Shamsi, A Preconditioner for the SOR-like Method for the Augmented Systems, Chiang Mai Journal ofScience,  39 (2012) 191-199.

 M. Bastani and D.K. Salkuyeh, Numerical studies of a non-local parabolic partial differential equations by spectral collocation method with preconditioning, Computational Mathematics and Modeling,   24 (2013) 81-89. 

 D. K. Salkuyeh, A short note on the paper ``Convergence of the TAGE iterative method for the system arisen from the cubic spline approximation for the solution of two-point BVPs with forcing function in integral form", by Mohanty, Jain and Dhall, Applied Mathematical Modelling, 36 (2012) 168-172.

D. K. Salkuyeh and S. Behnejad, Letter to the Editor regarding ``Modified Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems"" [Numer. Linear Algebra Appl. 14 (2007) 217-235]", Numerical Linear Algebra with Applications,  19 (2012) 885-890.


  D. K. Salkuyeh, On the solution of the fuzzy Sylvester equation, Soft Computing, 15 (2010) 953-961. 

 D. K. Salkuyeh, H. Roohani, Convergence of the Variational Iteration Method for the Telegraph Equation with Integral Conditions, Numerical Methods for Partial Differential Equations, 27 (2011) 1442-1455.

  D. K. Salkuyeh, A. Fahim, A New Iterative Refinement of the Solution of Ill-Conditioned Linear System of Equations, International Journal of Computer Mathematics, 88 (5) (2011) 950 – 956.

D. K. Salkuyeh, A Sparse Approximate Inverse Preconditioner for Nonsymmetric Positive Definite Matrices, Journal of  Applied Mathematics and Informatics, 28 (2010) 1131-1141.


 H. Roohani and D. K. Salkuyeh, New General Solutions for the General Elliptic and Auxiliary Equations and Application to the Coupled KdV Equation, International Journal of Computer Mathematics, 87 (12) (2010) 2760-2768.


D. K. Salkuyeh and F. Toutounian, Optimal Iterate of the Power and Inverse Iteration Methods, Applied Numerical Mathematics, 59 (2009) 1537-1548.

D. K. Salkuyeh and F. Toutounian, A Sparse-Sparse Iteration for Computing a Sparse Incomplete Factorization of the Inverse of an SPD Matrix, Applied Numerical Mathematics, 59 (2009) 1265-1273.




 1. Numerical Linear Algebra, Second Edition, 240 pages, Publisher: Guilan Academic Center for Education (http://gilan.acecr.ir/).

To buy the book please drop me a note at salkuyeh@gmail.com.


2. Numerical Methods in Linear Algebra (Second Edition) , 363 pages. Publisher: University of Guilan.

To buy the book please visit : http://www.ketabiran.ir
Errata to the first edition of the book. 

3. Iterative Methods for Solving Linear System of Equations (in persian), 213 pages. Publisher: Mowj-Chaharom.

To buy the book please visit: http://www.ketabiran.ir


My PhD students:

1-Mehdi Bastani, Images restoration by solving linear system of equations based on the HSS iterative method, Azarbaijan Shahid Madani University, Dr. Naser Aghazadeh (Supervisor), D. Khojasteh Salkuyeh (Advisor), Defense date: April, 2015.

2-Davod Hezari, SOR iterative method and its acceleration for solving complex symmetric of linear equations, Defense date: February 2016.

3. Vahid Edalatpour, On the preconditioning of complex system of linear equations, Defense date: June 5, 2016.

4. Mohsen Masoudi, Some results on preconditioning of the saddle point problems,  Defense date: Feb 26, 2019.

5. Tahereh Salimi Siahkolaei, 2016, Ongoing.

6. Maryam Rahimian, 2016, Ongoing.

7. Hamid Mirchi, 2017, Ongoing.

8. Maedeh pourbagher, 2018, Ongoing.

9. Hamed Aslani, 2018, Ongoing.

[ not available ]

Fall semester, 2015
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contact Dr. Davod Khojasteh Salkuyeh
Department of Mathematics, Faculty of Mathematical Sciences, P.O. Box 41335-1914, 1Rasht, Guilan, Iran
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