Dr. Emil **Cătinaș**

### Academic degree:

Ph.D. in Mathematics (1999)

### Current position:

Head of *Tiberiu Popoviciu Institute of Numerical Analysis* (ICTP)

Senior researcher (I) at ICTP

### Domains of research:

Current (for finding papers by category see bottom):

- Iterative methods for nonlinear problems
- Programming in MATLAB, Julia and C for numerical tests.
- Numerical Linear Algebra
- Krylov methods for solving large linear systems in R
^{n} - eigenproblems solved by Newton-type iterations

- Krylov methods for solving large linear systems in R
- Numerical methods of ordinary/partial differential equations (in progress)

Past:

- Computer graphics

### Recent/relevant/cited papers:

- E. Cătinaş,
*How many steps still left to x*?*, SIAM Rev. 63 (2021) no. 3, pp. 585–624 (posts allowing anonymous comments – soon). - E. Cătinaş,
*A survey on the high convergence orders and computational convergence orders of sequences*, Appl. Math. Comput.,**343**(2019) 1-20. - E. Cătinaş,
*The strict superlinear order can be faster than the infinite order*, Numer. Algor., (2023). https://doi.org/10.1007/s11075-023-01604-y - E. Cătinaş,
*Estimating the radius of an attraction ball*, Appl. Math. Lett.,**22**(2009) no. 5, pp. 712-714. - E. Cătinaş,
*The inexact, inexact perturbed and quasi-Newton methods are equivalent models*, Math. Comp.,**74**(2005) no. 249, pp. 291-301. - E. Cătinaş,
*On the superlinear convergence of the successive approximations method*, J. Optim. Theory Appl.,**113**(2002) no. 3, pp. 473-485. - E. Cătinaş,
*Inexact perturbed Newton methods and applications to a class of Krylov solvers*, J. Optim. Theory Appl.,**108**(2001) no. 3, pp. 543-570. - E. Cătinaş,
*On some iterative methods for solving nonlinear equations*, Rev. Anal. Numér. Théor. Approx.,**23**(1994) no. 1, pp. 47-53.

### Papers as posts by:

- name (Catinas)
- category: Numerical Analysis (all the papers from ICTP)
- year (2019,…,1994) (all the papers from ICTP)

**Personal Data**

Date and place of birth | 1967, Cluj-Napoca |

Marital status | Married (to Teodora) |

ecatinas[at]ictp.acad.ro |

**Education and degrees**

1999 | Ph.D. in Mathematical Analysis (with distinction Cum Laudae)Babeş-Bolyai University, Cluj-Napoca Thesis: Newton and Newton-Krylov methods for solving nonlinear systems in R^{n}Scientific advisor: acad. Dimitrie D. Stancu |

1990-1991 | Specialization, Babeş-Bolyai University, Cluj-Napoca |

1986-1990 | Faculty of Mathematics, Babeş-Bolyai University |

1981-1985 | Industrial Highschool no. 4, Cluj-Napoca |

**Employment history**

2007- | Senior Researcher (I) at Tiberiu Popoviciu Institute of Numerical Analysis (ICTP), Romanian Academy |

2001-2007 | Senior Researcher (II) at ICTP |

1996-2001 | Senior Researcher (III) at ICTP |

1992-1996 | Researcher at ICTP |

1991-1992 | Research assistant at ICTP |

**Managing activities**

Head of ICTP (2008-present)

Organizer of the International Conference *Semicentennial of T. Popoviciu Institute of Numerical Analysis (ICTP50)*.

Research contracts: coordinator of the following grants

- 2CEEX-06-11-96/19.09.2006, 2006-2008, (MEdC).
- GAR 11/2006 (Romanian Academy).
- GAR 16/2005 (Romanian Academy).
- GAR 16/2004 (Romanian Academy).
- GAR 19/2003 (Romanian Academy).
- GAR 45/2002 (Romanian Academy).
- GAR 64/2001 (Romanian Academy).
- MEC 7037/B3/2001(T) (CNCSIS).
- GANSTI 6100 GR/2000 (ANSTI).
- GAR 97/1999 (Romanian Academy).
- GAR 95/1998 (Romanian Academy).

**Teaching Experience**

- Seminars and laboratories taught at the Technical University Cluj-Napoca (numerical analysis, mathematical analysis, algebra, geometry) 1992-1993, 1999-2000;
- Seminars and laboratories taught at the ”Babeş-Bolyai” University Cluj-Napoca (numerical analysis, probabilities, statistics) 1994-1997, 2003-2004, 2006.

**Selected Talks at Meetings and Symposia**

- I. Păvăloiu, E. Cătinaş,
*On a Newton-Hermite-Steffensen method*, NAAT 2018, Cluj-Napoca. - I. Păvăloiu, E. Cătinaş,
*On a robust iterative method for solving nonlinear equations*, VIII Jaen Conference on Approximation, July 2nd – July 7th, 2017, Ubeda, Spain. - I. Păvăloiu, E. Cătinaş,
*Avantaje numerice ale monotoniei unor metode iterative (Numerical advantages of the monotony of some iterative methods)*, Zilele Academice Clujene, Simpozion “Metode numerice și de aproximare”, Cluj-Napoca, 20 mai 2015. - (with I. Păvăloiu),
*On the convergence of an Aitken-Newton type method*, Third International Conference on Numerical Analysis and Approximation Theory (NAAT 2014), September 17-20, 2014, Cluj-Napoca, Romania. - I. Păvăloiu, E. Cătinaş, Asupra unei metode iterative de tip interpolator pentru rezolvarea ecuaţiilor neliniare, Simpozion de Analiză Numerică şi Aproximare, Zilele Academice Clujene, 5 iunie 2014, Institutul de Calcul “T. Popoviciu”, Cluj-Napoca.
*On some convergence conditions for Newton type iterations*, Second International Conference on Numerical Analysis and Approximation Theory (NAAT 2010), September 23-26, 2010, Cluj-Napoca, Romania.- (with I. Păvăloiu),
*On a Newton-Steffensen-type method*, Second International Conference on Numerical Analysis and Approximation Theory (NAAT 2010), September 23-26, 2010, Cluj-Napoca, Romania. *The fast trajectories towards the fixed points: characterization and related results*, 9th IMACS International Symposium on Iterative Methods in Scientific Computing, March 17-20, 2008, Lille, France.*On the Newton-GMBACK method*, 9th IMACS International Symposium on Iterative Methods in Scientific Computing, March 17-20, 2008, Lille, France.*On a Steffensen-type method*, 9th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, September 26-29, 2007, Timisoara, Romania.- (chair of the session Numerical Methods)
*On the convergence of the Newton-GMBACK method*, International Conference on Engineering and Mathematics, Bilbao, Spain, July 9-11, 2007; *New results in local convergence of iterative methods for nonlinear systems and fixed point problems*, International Congress of Mathematicians, Madrid, August 22-30, 2006;- (chair of the session Computational Methods XV)
*On the local convergence of the quasi-Newton methods*, International Conference of Computational Methods in Sciences and Engineering, Loutraki, Greece, October 21-26, 2005; *The relationship between the models of perturbed iterations, with applications*, GAMM Annual Meeting, Luxembourg, March 28-April 1, 2005;*Estimating the radius of the attraction balls*, Dynamics Days 2004, Palma de Mallorca, Spain, September 13-17, 2004.- GAMM Workshop on Applied and Numerical Linear Algebra, July 2-3, 2004, Hagen, Germany.
*Approximation by successive substitutions: the fast trajectories and an acceleration technique*, 4th International Bommerholz Meeting on Constructive Approximation (IBoMat04), Witten-Bommerholz, Germany, February 15-20, 2004.*Characterizing the fast trajectories toward the fixed points*, Dynamics Days 2003, Palma de Mallorca, Spain, September 24-27, 2003.*Characterizing the high convergence orders of the successive approximations*, GAMM Workshop on Numerical and Applied Linear Algebra, Braunschweig University, Germany, September 12-13, 2003.*Characterizing the high convergence orders of the Newton-GMBACK method*, GAMM Workshop: Numerical Linear Algebra with special emphasis on Multilevel and Krylov Subspace Methods, Bielefeld University, Germany, September 13-14, 2002.*Newton-GMRES and -MINPERT behave asymptotically almost the same*, Computational Linear Algebra with Applications, Milovy, Czech Republic, August 4-10, 2002.*Some aspects in the convergence of a class of Newton-Krylov algorithms*, Latsis Symposium 2002 – Iterative Solvers for Large Linear Systems, Swiss Federal Institute of Technology (ETH) Zurich, Switzerland, February 17-24, 2002 (www.sam.math.ethz.ch/~mhg/CG50/).- (Invited talk in minisymposia)
*Some aspects in the convergence of the Newton-GMRES, -GMBACK and -MINPERT methods*at The First SIAM-EMS conference Applied Mathematics in our Changing World (AMCW01), Berlin, Germany, September 2-6, 2001. *Some semilocal convergence theorems for certain Chebyshev- and Newton-type methods for approximating the eigenpairs of matrices*, poster at the International Congress of Mathematics ICM98, Berlin, Germany, August 18-27, 1998.

**Membership in professional societies**

- Society for Industrial and Applied Mathematics (SIAM).
- GAMM Numerical and Applied Linear Algebra Group.
- Romanian Mathematical Society (SSMR).

**Other professional activities**

- Editor-in-Chief of
*Journal of Numerical Analysis and Approximation Theory*(Romania), 2015-present

(during 1995-2012, secretary of the Editorial Board, during 2012-2015, member of the Editorial Board). - Member of the editorial board of
*Southwest Journal of Pure and Applied Mathematics*(USA), 1996-2004; - Member of the editorial board of
*International Review of Pure and Applied Mathematics*(India), 2004-2005; - Member of the editorial board of
*Pacific-Asian Journal of Mathematics*(India), 2004-2005;

**Awards**

*Excellence Diploma of the Romanian Academy*, 2015, for outstanding results in Numerical Analysis.- “Al. Myller” Prize at the National Students Colloquium “Grigore Moisil” 1988, for the paper
*The representation of the parametrical surfaces using the depth-sorting method*. - The Faculty of Mathematics and Computer Science Prize at the Students Colloquium, 1988, for the paper
*The representation of the parametrical surfaces using the depth-sorting method*.

**Computer experience**

- Operating systems: Windows, Linux.
- Programming languages: Matlab, Julia, C, (Pascal).
- Word-processing languages: LaTeX, Scientific Work Place.

**Languages**

- English
- French.

**Note:** the publications may be consulted as posts, clickable by author (e.g., E. Catinas), category (either type, e.g., (original), (survey), paper, book or mathematical field, e.g., nonlinear systems in Rn, convergence orders), tag (year: 2019), etc.

The processing of the information is in progress.

**Survey-type papers:**

- E. Cătinaş,
*How many steps still left to x*?*, SIAM Rev. 63 (2021) no. 3, pp. 585–624. - E. Cătinaş,
*A survey on the high convergence orders and computational convergence orders of sequences*, Appl. Math. Comput.,**343**(2019) 1-20.

**Original papers:**

- N. Suciu, F.A. Radu, J.S. Stokke, E. Cătinaș, A. Malina,
*Computational orders of convergence of iterative methods for Richards’ equation,*arXiv:2402.00194v1, https://doi.org/10.48550/arXiv.2402.00194 - E. Cătinaş,
*The strict superlinear order can be faster than the infinite order*, Numer. Algor.,**95**(2024), pp. 1177–1186. https://doi.org/10.1007/s11075-023-01604-y - I. Păvăloiu, E. Cătinaș, A
*new optimal method of order four of Hermite-Steffensen type,*Mediterr. J. Math. (2022) 19:147 - I. Păvăloiu, E. Cătinaş,
*On a robust Aitken–Newton method based on the Hermite polynomial*, Appl. Math. Comput.,**287-288**(2016), pp. 224-231. - E. Cătinaş,
*On the convergence of some quasi-Newton iterates studied by I. Păvăloiu*, J. Numer. Anal. Approx. Theory,**44**(2015) no. 1, pp. 38-41. - I. Păvăloiu, E. Cătinaş,
*On a Newton-Steffensen type method*, Appl. Math. Lett., 26 (2013) no. 6, pp. 659-663 (tech. rep. here). - I. Păvăloiu, E. Cătinaş,
*On an Aitken-Newton type method*, Numer. Algor.,**62**(2013) no. 2, pp. 253-260 (tech. rep. here). - I. Păvăloiu, E. Cătinaş,
*Bilateral approximations for some Aitken-Steffensen-Hermite type methods of order three*, Appl. Math. Comput.,**217**(2011) 12, pp. 5838-5846 (tech. rep. here). - I. Păvăloiu, E. Cătinaş,
*On a Steffensen-Hermite method of order three*, Appl. Math. Comput., 215 (2009) 7, pp. 2663-2672 (tech. rep. here). - E. Cătinaş,
*Estimating the radius of an attraction ball*, Appl. Math. Lett.,**22**(2009) no. 5, pp. 712-714 (freely available at ScienceDirect; tech. rep. here). - I. Păvăloiu, E. Cătinaş,
*On an Aitken type method*, Rev. Anal. Numér. Théor. Approx., 36 (2007) no. 2, pp. 173-176 (pdf file also here). - E. Cătinaş,
*The inexact, inexact perturbed and quasi-Newton methods are equivalent models*, Math. Comp.,**74**(2005) no. 249, pp. 291-301 (freely available at AMS; pdf file also here). - E. Cătinaş,
*On the superlinear convergence of the successive approximations method*, J. Optim. Theory Appl.,**113**(2002) no. 3, pp. 473-485. (tech. rep. here). - E. Cătinaş,
*Affine invariant conditions for the inexact perturbed Newton method*, Rev. Anal. Numér. Théor. Approx., 31 (2002) no. 1, pp. 17-20. (pdf file also here). - E. Cătinaş, I. Păvăloiu,
*On a third order iterative method for solving polynomial operator equations*, Rev. Anal. Numér. Théor. Approx., 31 (2002) no. 1, pp. 21-28. (pdf file also here). - E. Cătinaş,
*Inexact perturbed Newton methods and applications to a class of Krylov solvers*, J. Optim. Theory Appl.,**108**(2001) no. 3, pp. 543-570. (tech. rep. here). - E. Cătinaş,
*On accelerating the convergence of the successive approximations method*, Rev. Anal. Numér. Théor. Approx., 30 (2001) no. 1, pp. 3-8. - E. Cătinaş,
*A note on the quadratic convergence of the inexact Newton methods*, Rev. Anal. Numér. Théor. Approx.,**29**(2000) no. 2, pp. 129-133. - I. Argyros, E. Cătinaş, I. Păvăloiu,
*Perturbed-Steffensen-Aitken projection methods for solving equations with nondifferentiable operators*, Punjab Univ. J. Math. (Lahore), 33 (2000), pp. 105-113. - I. Argyros, E. Cătinaş, I. Păvăloiu,
*On the convergence of Steffensen-Aitken-like methods using divided differences obtained recursively*, Adv. Nonlinear Var. Inequal., 3 (2000) no. 1, pp. 7-13. - I. Argyros, E. Cătinaş, I. Păvăloiu
*On the approximate solutions of implicit functions using the Steffensen method*, Proyecciones, 19 (2000) no. 3, pp. 291-303 (MR 2001k:65096) (pdf file also here) - I. Argyros, E. Cătinaş, I. Păvăloiu
*On some general iterative methods for solving nonlinear operator equations containing a nondifferentiable term*, Adv. Nonlinear Var. Inequal., 3 (2000) no. 1, pp. 15-21. - I. Argyros, E. Cătinaş, I. Păvăloiu,
*Conditions for the convergence of perturbed Steffensen methods on a Banach space with a convergence structure*, Adv. Nonlinear Var. Inequal., 3 (2000) no. 1, pp. 23-35. - I. Argyros, E. Cătinaş, I. Păvăloiu,
*Local and global convergence results for a class of Steffensen-Aitken-type methods*, Adv. Nonlinear Var. Inequal., 2 (1999) no. 2, pp. 117-126. (MR2000d:65094) - I. Păvăloiu, E. Cătinaş,
*Remarks on some Newton and Chebyshev-type methods for approximation eigenvalues and eigenvectors of matrices*, Comput. Sci. J. Mold., 7 (1999) no.1, pp. 3-15 (pdf file also here). - E. Cătinaş,
*On the high convergence orders of the Newton-GMBACK methods*, Rev. Anal. Numér. Théor. Approx., 28 (1999) no. 2, pp. 125-132. (MR 2002c:65054) - E. Cătinaş, I. Păvăloiu,
*On some interpolatory iterative methods for the second degree polynomial operators (II)*, Rev. Anal. Numér. Théor. Approx., 28 (1999) no. 2, pp. 133-143 (pdf file also here). - E. Cătinaş,
*On the r-convergence orders of the inexact perturbed Newton methods*, Bul. ştiinţ. Univ. Baia Mare, Ser. B, Mat. Inf., 15 (1999) no. 1-2, pp. 75-78. - I. Argyros, E. Cătinaş, I. Păvăloiu,
*Improving the rate of convergence of some Newton-like methods for the solution of nonlinear equations containing a nondifferentiable term*, Rev. Anal. Numér. Théor. Approx., 27 (1998) no. 2, pp. 191-202. - E. Cătinaş, I. Păvăloiu,
*On some interpolatory iterative methods for the second degree polynomial operators (I)*, Rev. Anal. Numér. Théor. Approx., 27 (1998) no. 1, pp. 33-45. - E. Cătinaş, I. Păvăloiu,
*On approximating the eigenvalues and eigenvectors of linear continuous operators*, Rev. Anal. Numér. Théor. Approx., 26 (1997) nos. 1-2, pp. 19-27 (pdf file also here). - E. Cătinaş, I. Păvăloiu,
*On the Chebyshev method for approximating the eigenvalues of linear operators*, Rev. Anal. Numér. Théor. Approx., 25 (1996) nos. 1-2, pp. 43-56 (pdf file also here). - E. Cătinaş,
*A note on inexact secant methods*, Rev. Anal. Numér. Théor. Approx., 25 (1996) nos. 1-2, pp. 33-41 (MR 99f:65077) (pdf file also here). - E. Cătinaş,
*On some Steffensen-type iterative methods for a class of nonlinear equations*, Rev. Anal. Numér. Théor. Approx., 24 (1995) nos. 1-2, pp. 37-43 (paper website; pdf file also here). - E. Cătinaş,
*On some iterative methods for solving nonlinear equations*, Rev. Anal. Numér. Théor. Approx., 23 (1994) no. 1, pp. 47-53 (link to the journal; pdf file also here). - E. Cătinaş,
*The representation of the parametrical surfaces using the depth-sorting method*, University of Cluj-Napoca, Faculty of Mathematics and Physics, Research Seminars, Seminar on Computer Science, Preprint no. 9 (1989), pp. 103-117.

**Proceedings**

- E. Cătinaş,
*On the nonmonotone behavior of the Newton-GMBACK method*, AIP Conf. Proc., 2008, vol. 1046, pp. 87-90. - I. Păvăloiu, E. Cătinaş,
*On a Steffensen type method*, IEEE Proceedings, 2007, pp. 369-375 (tech. rep. here). - E. Cătinaş,
*On the convergence of the Newton-GMBACK method*, 2007 International Conference on Engineering and Mathematics, Bilbao, Spain, July 9-11, 2007, pp. 11-14, ISBN 978-84-95809-29-2. - E. Cătinaş,
*The relationship between the models of perturbed Newton iterations, with applications*, PAMM, 5 (2005) no. 1, pp. 785-786. (journal website) - E. Cătinaş,
*Sufficient convergence conditions for certain accelerated successive approximations*, Trends and Applications in Constructive Approximation, M.G. de Bruin, D.H. Mache and J. Szabados (eds.), International Series of Numerical Mathematics, vol. 1, pp. 71-75, 2005, Birkhauser Verlag, Basel (pdf file also here). - E. Cătinaş, I. Păvăloiu,
*On the Chebyshev method with numerical applications to the eigenpair problem*, An. Univ. Timisoara Ser. Mat.-Inform., 41 (2003), special issue, pp. 183-190. - E. Cătinaş, I. Păvăloiu,
*On the Chebyshev method with numerical applications to the eigenpair problem*, Symbolic and Numeric Algorithms for Scientific Computations (SYNASC03), Proceedings of the 5th International Workshop, Timisoara, Romania, October 1-4, D. Petcu, V. Negru, D. Zaharie and T. Jebelean (eds.), pp. 204-210, 2003, ISBN 973-585-785-5. - E. Cătinaş, I. Păvăloiu,
*Solving polynomial operator equations of degree 2 by Steffensen-type iterations with approximate inverses*, Proceedings of the International Symposium on Numerical Analysis and Approximation Theory, May 9-11, Cluj-Napoca, 2002, R. Trimbitas (ed.), pp. 101-113. ISBN 973-610-166-5. - E. Cătinaş, I. Păvăloiu,
*Some numerical aspects in the approximation of eigenpairs of matrices by the Newton method*, Acta Technica Napocensis, Series: Applied Mathematics and Mechanics, 42 (1999) vol. I, pp. 41-44. - E. Cătinaş, I. Păvăloiu,
*On a Chebyshev-type method for approximating the solutions of polynomial operator equations of degree 2*, Approximation and Optimization, Proceedings of the International Congress on Approximation and Optimization (Romania)-ICAOR, Cluj-Napoca, July 29-August 1, 1996, vol. I, pp. 219-226, D. D. Stancu, Gh. Coman, W. W. Breckner and P. Blaga (eds.), Transilvania Press, 1997 (MR 99f:65084) ISBN 973-98180-7-2.

**PhD thesis**

title: *Metode de tip Newton şi Newton-Krîlov în rezolvarea sistemelor neliniare din Rⁿ
(Methods of Newton and Newton-Krylov type for solving nonlinear systems in Rⁿ)*,

year: 1999,

scientific advisor: acad. Dimitrie D. Stancu, Faculty of Mathematics and Computer Science, “Babes-Bolyai” University

(appreciated by the scientific committee with distinction

*Cum Laudae*);

**Other works**

- E. Cătinaş,
*Istoricul Institutului de Calcul “Tiberiu Popoviciu”*, (in Romanian, for the moment) https://ictp.acad.ro/ro/istoric (to be finalized) - E. Cătinaş,
*Tiberiu Popoviciu*website (https://ictp.acad.ro/tiberiu-popoviciu, under construction) - E. Cătinaș, N. Suciu,
*In memoriam dr. Călin Vamoș, member of Tiberiu Popoviciu Institute of Numerical Analysis*, J. Numer. Anal. Approx. Theory,**46**(2017) no 1, pp. 107-109. - E. Cătinaș, I. Păvăloiu,
*Professor Costică Mustăța at his 75th anniversary*, J. Numer. Anal. Approx. Theory,**46**(2017) no 1, pp. 3-5. - E. Cătinaş,
*A new name for an old journal*, J. Numer. Anal. Approx. Theory,**44**(2015) no. 1, pp. 3-6. - E. Cătinaş,
*Professor Ion Păvăloiu at his 75th anniversar**y,*J. Numer. Anal. Approx. Theory,**44**(2015) no. 1, pp. 7-10. - E. Cătinaş,
*Poate un institut “mic” să devină “mare”?*, Zilele Academice Clujene, nr. 1, iunie 2014, editat de Asociaţia Ars Transsilvaniae România, sub egida Academiei Române Filiala Cluj-Napoca.

[English title:*Can a “small” institute become “big”?*] - I. Păvăloiu, E. Cătinaş,
*In memoriam professor Dimitrie D. Stancu, honorary member of the Romanian Academy*, Rev. Anal. Numér. Théor. Approx.,**43**(2014) no. 2, pp. 93-102. - E. Cătinaş,
*Profesorul emerit D.D. Stancu, membru de onoare al Academiei Române, la vârsta de 85 de ani*, Academica, anul XXII (266) 2012, nr. 12. - E. Cătinaş, C. Mustăţa,
*Professor Ion Păvăloiu at his 70th anniversary*, Rev. Anal. Numér. Théor. Approx.,**38**(2009) no. 2, pp. 113-114. - I. Păvăloiu, E. Cătinaş,
*The international conference “Semicentennial T. Popoviciu Institute of Numerical Analysis”, May 7-10, 2008*, Rev. Anal. Numér. Théor. Approx.,**37**(2008) no. 2, pp. 107-108.

The results may be retrieved as posts, categorized by the following subjects:

(work in progress)

Version of August 5, 2023.