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Emil Cătinaş
Publications

Books:

• Methods of Newton and Newton-Krylov type, Risoprint, Cluj-Napoca, 2007, XVI + 177 pp., ISBN 978-973-751-533-9.

In ISI journals:

• (with I. Păvăloiu), On a Steffensen-Hermite method of order three, Applied Mathematics and Computation, 215 (2009) 7, pp. 2663-2672 (tech. rep. here).
• Estimating the radius of an attraction ball, Applied Mathematics Letters, 22 (2009) no. 5, pp. 712-714, (technical report here).
• The inexact, inexact perturbed and quasi-Newton methods are equivalent models, Math. Comp., 74 (2005) no. 249, pp. 291-301 (tech. rep. here).
• On the superlinear convergence of the successive approximations method, J. Optim. Theory Appl., vol. 113 (2002) no. 3, pp. 473-485 (tech. rep. here).
• Inexact perturbed Newton methods and applications to a class of Krylov solvers, J. Optim. Theory Appl., vol. 108 (2001) no. 3, pp. 543-570 (tech. rep. here).
• On the Nonmonotone Behavior of the Newton-Gmback Method, AIP Conf. Proc., September 17, 2008, vol. 1046, pp. 87-90, ISBN 978-7354-0574-5 (ISI Proceedings).
• (with I. Păvăloiu), On a Steffensen type method, 9th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Timisoara, Romania, September 26-29, 2007, IEEE Proceedings, pp. 369-375, ISBN 0-7695-3078-8 (ISI Proceedings).

In international journals:

• The relationship between the models of perturbed Newton iterations, with applications, PAMM, 5 (2005) no. 1, pp. 785-786.
• (with I. Argyros and I. Păvăloiu) Perturbed-Steffensen-Aitken projection methods for solving equations with nondifferentiable operators, Punjab Univ. J. Math. (Lahore), 33 (2000), pp. 105-113.
• (with I. Argyros and I. Păvăloiu) On the convergence of Steffensen-Aitken-like methods using divided differences obtained recursively, Adv. Nonlinear Var. Inequal. (SUA), 3 (2000) no. 1, pp. 7-13.
• (with I. Argyros and I. Păvăloiu) On the approximate solutions of implicit functions using the Steffensen method, Proyecciones, 19 (2000) no. 3, pp. 291-303, Universidad Catolica del Norte, Antofagasta, Chile. (MR 2001k:65096).
• (with I. Argyros and I. Păvăloiu) On some general iterative methods for solving nonlinear operator equations containing a nondifferentiable term, Adv. Nonlinear Var. Inequal. (SUA), 3 (2000) no. 1, pp. 15-21.
• (with I. Argyros and I. Păvăloiu) Conditions for the convergence of perturbed Steffensen methods on a Banach space with a convergence structure, Adv. Nonlinear Var. Inequal. (SUA), 3 (2000) no. 1, pp. 23-35.
• (with I. Argyros and I. Păvăloiu) Local and global convergence results for a class of Steffensen-Aitken-type methods, Adv. Nonlinear Var. Inequal. (SUA), 2 (1999) no. 2, pp. 117-126. (MR2000d:65094)
• (with I. Păvăloiu) Remarks on some Newton and Chebyshev-type methods for approximating the eigenvalues and eigenvectors of matrices, Computer Science Journal of Moldova, 7 (1999) no.1, pp. 3-15. (MR 2001c:65044)

In proceedings of international conferences:

• 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.
• Sufficient convergence conditions for certain accelerated successive approximations, Trends and Applications in Constructive Approximation, Eds. M.G. de Bruin, D.H. Mache and J. Szabados, International Series of Numerical Mathematics, vol. 1, pp. 71-75, 2005, Birkhauser Verlag, Basel, ISBN 3-7643-7124-2, (tech. rep. here).

In journals edited by the Romanian Academy

• On an Aitken type method, Rev. Anal. Numér. Théor. Approx., 36 (2007) no. 2, pp. 173-176.
• Affine invariant conditions for the inexact perturbed Newton method, Rev. Anal. Numér. Théor. Approx., 31 (2002) no. 1, pp. 17-20.
• (with 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.
• On accelerating the convergence of the successive approximations method, Rev. Anal. Numér. Théor. Approx., 30 (2001) no. 1, pp. 3-8 (tech. rep. here).
• A note on the quadratic convergence of the inexact Newton methods, Rev. Anal. Numér. Théor. Approx., 29 (2000) no. 2, pp. 129-134.
• 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).
• (with 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.
• (with I. Argyros and 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.
• (with 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. (MR CMP 1 818 213)
• (with 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.
• (with 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. (MR 99d:65172)
• A note on inexact secant methods, Rev. Anal. Numér. Théor. Approx., 25 (1996) nos. 1-2, pp. 33-41. (MR 99f:65077)
• 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.
• On some iterative methods for solving nonlinear equations, Rev. Anal. Numér. Théor. Approx., 23 (1994) no. 1, pp. 47-53. (MR 96f:65071)

In other proceedings of international conferences

• (with 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.
• (with 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.
• (with 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.

In journals edited by Romanian Universities

• (with I. Păvăloiu), Some numerical aspects in approximating the eigenpairs by Newton methods, Acta Technica Napocensis, Series: Applied Mathematics and Mechanics, 42 (1999) vol. I, pp. 41-44.
• 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.
• 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.

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