RESEARCH
My research work concerns the study of iterative methods to solve nonlinear equations,
mainly in a theoretical way. So most of my results have been given in Banach spaces.
I have studied the convergence of Newton's method in Banach spaces (Newton-Kantorovich
theorem) and also other iterative processes such as Chebysev's, Halley's or
super-Halley's. Another branch of my research is connected with the dynamical study of
some methods for solving nonlinear equations.
In 1995, I finished my Ph. D. Thesis (in Spanish) Newton's method in Banach spaces.
It was directed by
Prof. Dr. Miguel
Ángel Hernández. Since then, I have been working in colaboration with
him and other members of his research group:
Amparo Salanova,
José Antonio Ezquerro,
María Jesús Rubio and
Natalia Romero. All of us make up the research team
PRIENOL (PRocesos Iterativos y Ecuaciones NO Lineales)
at the University of La Rioja. You can have a look to
our homepage for more information.
In addition, I collaborate usually with the two Dominican doctors,
Manuel Aurelio Diloné Alvarado y Martín García Olivo,
who developed his PhD under my supervision.
In this page you can find:
- Articles published in scientific journals.
- Selected lectures presented in congresses (5 last years).
- PhD Thesis that I have supervised.
You can get more information about my articles by visiting
my page in MathSciNet or the database
Zentralblatt Math.
If you are interested in any of my papers, let me know
by sending me an email and I'll send them
to you as soon as possible.
1. Published articles
- 1995
- J. M. Gutiérrez, M. A. Hernández and M. A. Salanova
-
Accesibility of solutions by Newton's method
International Journal of Computer Mathematics, Vol. 57, pp. 239-247.
- 1996
- J. M. Gutiérrez, M. A. Hernández and M. A. Salanova
- Resolution of quadratic equations in Banach spaces
Numerical Functional Analysis and Optimization, Vol. 17, No. 1-2, pp. 113-121.
- 1997
- J. M. Gutiérrez and M. A. Hernández
-
A family of Chebyshev-Halley type methods in Banach spaces
Bulletin of the Australian Mathematical Society, Vol. 55, pp. 113-130.
- J. M. Gutiérrez
-
A new semilocal convergence theorem for Newton's method
Journal of Computational and Applied Mathematics, Vol. 79, pp. 131-145.
- J. M. Gutiérrez and M. A. Hernández
-
Third order methods for operators with bounded second derivative
Journal of Computational and Applied Mathematics, Vol. 82, pp. 171-183.
- J. M. Gutiérrez and M. A. Hernández
-
New recurrence realtions for Chebyshev method
Applied Mathematics Letters, Vol. 10, No. 2, pp. 63-65.
- J. A. Ezquerro, J. M. Gutiérrez and M. A. Hernández
-
A construction procedure of iterative methods with cubical convergence
Applied Mathematics and Computation, Vol. 85, pp. 181-199.
- 1998
- J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández and
M. A. Salanova
-
The application of an inverse-free Jarratt type approximation to nonlinear integral
equations of Hammerstein type
Computers and Mathematics with Applications, Vol. 36, No. 4, pp. 9-20.
- J. A. Ezquerro, J. M. Gutiérrez and M. A. Hernández
-
A construction procedure of iterative methods with cubical convergence II: another
convergence approach
Applied Mathematics and Computation, Vol. 92, pp. 59-68.
- J. A. Ezquerro, J. M. Gutiérrez and M. A. Hernández
-
Solving a nonlinear equation by a uniparametric family of iterative processes
International Journal of Computer Mathematics, Vol. 68, pp. 301-308.
- J. M. Gutiérrez and M. A. Hernández
-
Majorizing sequences for Newton's method
Tamkang Journal of Mathematics, Vol. 29, No. 3, pp. 199-202.
- J. M. Gutiérrez and M. A. Hernández
-
New recurrence realtions for the super-Halley method
Computers and Mathematics with Applications, Vol. 36, No. 7, pp. 1-8.
- 1999
- J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández and
M. A. Salanova
-
Chebyshev-like methods and quadratic equations
Revue d'Analyse Numerique et theorie de l'Approximation, Vol. 28, No. 1, pp. 23-35.
- J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández and
M. A. Salanova
-
Solving nonlinear equations arising in radiative transfer
Numerical Functional Analysis and Optimization, Vol. 20, No. 7-8, pp. 661-673.
- 2000
- J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández and
M. A. Salanova
-
A biparametric family of inverse-free multipoint iterations
Computational and Applied Mathematics, Vol. 19, No. 1, pp. 109-124.
- J. M. Gutiérrez and M. A. Hernández
- Newton's method under weak Kantorovich conditions
IMA Journal of Numerical Analysis, Vol. 20, pp. 521-532.
- 2001
- J. M. Gutiérrez and M. A. Hernández
- Newton's method under different Lipschitz conditions
Proceedings of the Second Conference on Numerical Analysis and Applications.
Rousse, Bulgaria, June 2000.
Lecture Notes in Computer Science, Vol. 1988, pp.368-376.
- J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández and
M. A. Salanova
- Halley's method: perhaps the most rediscovered method in the world
Margarita Mathematica (homage to José Javier Guadalupe, Chicho)
Servicio de Publicaciones de la Universidad de La Rioja, pp. 205-220.
- M. Benito, J. M. Gutiérrez and V. Lanchares
- Chicho's fractal
Margarita Mathematica (homage to José Javier Guadalupe, Chicho)
Servicio de Publicaciones de la Universidad de La Rioja, pp. 247-254.
- J. M. Gutiérrez, M. A. Hernández and M. A. Salanova
- Calculus of nth roots and third order iterative methods
Nonlinear Analysis, Vol. 47, pp. 2875--2880.
- 2003
- S. Amat, S. Busquier and J. M. Gutiérrez
- Geometric constructions of iterative functions to solve nonlinear equations
Journal of Computational and Applied Mathematics, Vol. 157, pp. 197--205.
- 2004
- J. M. Gutiérrez, M. A. Hernández and M. A. Salanova
- alpha-theory for nonlinear Fredholm integral equations
Grazer Mathematische Berrichte (Graz Mathematical Reports), Vol. 346, pp. 187--196.
- S. Amat, S. Busquier and J. M. Gutiérrez
- On the local convergence theorem of secant-type methods
International Journal of Computer Mathematics, Vol. 81, no. 8, pp. 1153--1161.
- J. M. Gutiérrez, M. A. Hernández and M. A. Salanova
- On the approximate solution of some Fredholm integral equations by Newton's method
Southwest Journal of Pure and applied Mathematics, Vol. 1 (July 04), pp. 1--9.
- 2005
- I. K. Argyros and J. M. Gutiérrez
- A unified approach for enlarging the radius of convergence for Newton's
method and applications
Nonlinear Functional Analysis and Applications, Vol 10, No. 4, pp. 555--563.
- 2006
- I. K. Argyros and J. M. Gutiérrez
- On the convergence of Newton-like methods under general and unifying conditions
Fixed Point Theory and Applications. Ed. Nova Science Publishers, Inc., Nueva York.
ISBN: 1-59454-873-0
- I. K. Argyros and J. M. Gutiérrez
- On the semilocal convergence of Newton's method under unifying conditions
Fixed Point Theory and Applications. Ed. Nova Science Publishers, Inc., Nueva York.
ISBN: 1-59454-877-3
- S. Amat, S. Busquier and J. M. Gutiérrez
- A new semilocal convergence theorem for Steffensen's method
International Journal of Applied Science and Computations, Vol 13, No. 1, pp. 14--19.
- S. Amat, S. Busquier and J. M. Gutiérrez
- An adaptative version of a fourth order iterative method for quadratic equations
Journal of Computational and Applied Mathematics, Vol 191, No. 2, pp. 259--268.
- 2007
- I. K. Argyros and J. M. Gutiérrez
- A unifying local and semilocal convergence analysis of Newton-like methods
Advances in nonlinear variational inequalities, Vol 10, No. 1, pp. 1--11.
- M. Grau, M. Peris and J. M. Gutiérrez
- Accelerated iterative methods for finding solutions of a systems of nonlinear equations
Applied Mathematics and Computation, Vol 190, pp. 1815--1823.
- 2008
- J. M. Gutiérrez, M. A. Hernández y N. Romero
- A note on a Modification of a Moser's method
Journal of Complexity, Vol 24, No. 2, pp. 185--197.
- V. Petuya, J. M. Gutiérrez, A. Alonso, O. Altuzarra y A. Hernández
- A numerical procedure to solve non-linear kinematic problems in spatial mechanisms
International Journal for Numerical Methods in Engineering, Vol 73, No. 6, pp. 825--843.
- J. M. Gutiérrez, M. A. Hernández, P. J. Miana y N. Romero
- New identities in the Catalan triangle
Journal of Mathematical Analysis and Applications, Vol 341, No. 1, pp. 52--61.
- S. Amat, S. Busquier, J. M. Gutiérrez y M. A. Hernández y N. Romero
- On the global convergence of Chebyshev's iterative method.
Journal of Computational and Applied Mathematics, Vol 220, pp. 17--21.
- 2009
- M. Grau y J. M. Gutiérrez
- Zero-finder methods derived from Obreshkov's techniques.
Applied Mathematics and Computation, Vol 215, No. 8, pp. 2992--3001.
- 2010
- J. M. Gutiérrez, M. A. Hernández y N. Romero
- Dynamics of a new family of iterative processes for quadratic polynomials
Journal of Computational and Applied Mathematics, Vol 233, pp. 2688--2695.
- M. Grau y J. M. Gutiérrez
- Some variants of the Chebyshev-Halley family of methods with fifth-order of convergence.
International Journal of Computer Mathematics, Vol 87, No. 4, pp. 818--833.
- M. Grau, M. Noguera y J. M. Gutiérrez
- On some computational orders of convergence.
Applied Mathematics Letters, Vol 23, pp. 472--478.
- J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández, N. Romero y M. J. Rubio
- El método de Newton: de Newton a Kantorovich.
La Gaceta de la RSME, Vol 13, No. 1, pp. 53--76.
- J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández, N. Romero y M. J. Rubio
- Relaciones de recurrencia en el método de Newton-Kantorovich
Contribuciones científicas en honor de Mirian Andrés Gómez,
Servicio de publicaciones de la Universidad de La Rioja, pp. 319--333.
- J. M. Gutiérrez, M. A. Hernández y N. Romero
- Alpha-theory for Newton-Moser method
Proceedings of the Tenth International Conference Zaragoza-Pau of applied Mathematics and Statisitics,
Monografías matemáticas García de Galdeano de la Universidad de Zaragoza, pp. 155--162.
- 2011
- S. Amat, S. Busquier y J. M. Gutiérrez
- Third order iterative methods with applications to Hammerstein equations: A unified approach
Journal of Computational and Applied Mathematics, Vol 235, pp. 2936--2943.
- I. K. Argyros, J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández y S. Hilout
- On the semilocal convergence of efficient Chebyshev-Secant-type methods
Journal of Computational and Applied Mathematics, Vol 235, pp. 3195--3206.
- M. A. Diloné y J. M. Gutiérrez
- A comparative study of different semilocal convergence results applied to Kepler's equation
Computational Mathematics: Theory, methods and Applications, Nova Science Publishers, Inc. pp. 201--211
Nueva York. ISBN: 978-1-60876-271-2.
- J. M. Gutiérrez, Á Magreñán y J. L. Varona
- The ''Gauss-Seidelization'' of iterative methods for solving nonlinear equations in the complex plane
Applied Mathematics and Computation, Vol 218, pp. 2467--2479.
- 2012
- J. M. Gutiérrez, S. PLaza y N. Romero
- Dynamics of a fifth-order iterative method
International Journal of Computer Mathematics, Vol 89, pp. 822--835.
- M. García-Olivo y J. M. Gutiérrez
- La obra "El cálculo de las raíces de una ecuación" de P. L. Chebyshev
Editorial Académica Española, LAMBERT Academic Publishing GmbH Co. KG. pp. 1--84
Alemania. ISBN: 978-3-659-02010-0.
- M. A. Diloné, M. García-Olivo y J. M. Gutiérrez
- A note on the semilocal convergence of Chebyshev's method
Bulletin of the Australian Mathematical Society, Vol 88, pp. 98--105.
- M. Grau, M. Noguera y J. M. Gutiérrez
- Frozen iterative methods using divided differences "à la Schmidt-Schwetlick".
Journal of Optimization Theory and Applications, pp. 1--18.
- 2013
- I. K. Argyros, J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández y S. Hilout
- Chebyshev-Secant-type methods for non-differentiable operators
Milan Journal of Mathematics, Vol 81, pp. 25--35.
- F. Chicharro, A. Cordero, J. M. Gutiérrez y J. R. Torregrosa
- Complex dynamics of derivative-free methods for nonlinear equations
Applied Mathematics and Computation, Vol 219, pp. 7023--7035.
- M. A. Diloné y J. M. Gutiérrez
- On the existence of attractive cycles for Newton's method applied to Kepler's equation
Journal of Advanced Research in Applied Mathematics, Vol 5, pp. 72--79.
- M. García-Olivo y J. M. Gutiérrez
- Notas históricas sobre el método de Chebyshev para resolver ecuaciones no lineales
Miscelánea Matemática, Vol 57, pp. 63--83.
- J. M. Gutiérrez, Á. A. Magreñán y N. Romero
- On the semilocal convergence of Newton-Kantorovich method under center-Lipschitz conditions.
Applied Mathematics and Computation, Vol 221, pp. 79--88.
- 2014
- J. M. Gutiérrez, L. J. Hernández, M. Marañón and M. T. Rivas
- Influence of the multiplicity of the roots on the basins of attraction of Newton's method.
Numerical Algorithms, Vol 66, pp. 431--455.
- M. Grau, M. Noguera and J. M. Gutiérrez
- Frozen iterative methods using divided differences a la Schmidt-Schwetlick.
Journal of Optimization Theory and Applications, Vol 160, pp. 931--948.
- I. K. Argyros, J. M. Gutiérrez, Á. A. Magreñán and N. Romero
- Convergence of the relaxed Newton's method.
Journal of the Korean Mathematical Society, Vol 51, pp. 137--162.
- Á. A. Magreñán, A. Cordero, J. M. Gutiérrez and J. R. Torregrosa
- Real qualitative behavior of a fourth-order family of iterative methods by using the
convergence plane.
Mathematics and Computers in Simulation, Vol 105, pp. 49--61.
- J. A. Ezquerro, D. González, J. M. Gutiérrez, M. A. Hernández,
Á. A. Magreñán, N. Romero and M. J. Rubio
- Resolución de ecuaciones no lineales mediante procesos iterativos.
Zubía, Monográfico Núm. 26, pp. 165--200.
- 2015
- J. M. Gutiérrez and Á. A. Magreñán
- Real dynamics for damped Newton's method applied to cubic polynomials.
Journal of Computational and Applied Mathematics, Vol 275, pp. 527--538.
- J. M. García-Calcines, J. M. Gutiérrez, L. J. Hernández
and M. T. Rivas
- Graphical representations for the homogeneous bivariate Newton's method.
Applied Mathematics and Computation, Vol. 269, pp. 988--1006.
- M. García-Olivo, J. M. Gutiérrez and
Á. A. Magreñán
- A complex dynamical approach of Chebyshev's method.
SeMA Journal, Vol. 71, pp. 57--68.
- J. M. Gutiérrez
- Numerical Properties of Different Root-Finding Algorithms Obtained for Approximating
Continuous Newton's Method.
Algorithms, Vol. 8, pp. 1210--1218.
- 2016
- J. C. Yakoubsohn, J. M. Gutiérrez and Á. A. Magreñán
- Complexity of an homotopy method at the neighbourhood of a zero.
Advances in Iterative methods for Nonlinear Equations,
SEMA SIMAI Springer series (Editores: S. Amat y S. Busquier), pp. 147--171.
- J. M. Gutiérrez, L. J. Hernández, Á. A. Magreñán
and M. T. Rivas
- Measures of the basins of attracting n-cycles for the relaxed Newton's method.
Advances in Iterative methods for Nonlinear Equations,
SEMA SIMAI Springer series (Editores: S. Amat y S. Busquier), pp. 211--245.
- A. Cordero, J. M. Gutiérrez,
Á. A. Magreñán and J. R. Torregrosa
- Stability analysis of a parametric family of iterative methods for solving nonlinear models.
Applied Mathematics and Computation, Vol. 285, pp. 26--40.
- J. M. Gutiérrez
- El problema de Cayley y el método de Chebyshev.
La Gaceta de la RSME, Vol. 19, p. 542.
- 2017
- M. García-Olivo, J. M. Gutiérrez and
Á. A. Magreñán
- A first overview on the real dynamics of Chebyshev's method.
Journal of Computational and Applied Mathematics, Vol. 318 pp.422--433.
- M. Grau, M. Noguera and J. M. Gutiérrez
- A multidimensional generalization of some classes of iterative methods.
SeMA Journal, Vol. 74 (1), pp. 57--73.
2. Last selected lectures in congresses (Last few years)
- M. Grau y J. M. Gutiérrez
- Métodos para resolver ecuaciones no lineales obtenidos a partir de métodos
para resolver ecuaciones diferenciales ordinarias
Congreso RSME 2009
Oviedo (February 2009).
- M. García Olivo y J. M. Gutiérrez
- Estudio dinámico del método de Chebyshev para polinomios cúbicos
Congreso RSME 2009
Oviedo (February 2009).
- J. M. Gutiérrez, Á. A. Magreñán y N. Romero
- Newton-Kantorovich theory under centered Lipschitz conditions
2010 Annual Meeting of the Italian Society for Industrial and Applied Mathematics
Cagliari (Italia) (June 2010).
- J. M. Gutiérrez, A. Magreñán y N. Romero
- A dynamic and analytical study of the damped Newton's method
Seventh International Conference on Engineering Computational Technology
Valencia (June 2010).
- S. Amat, S. Busquier y J. M. Gutiérrez
- On the application of iterative methods for geometric problems
Seventh International Conference on Engineering Computational Technology
Valencia (June 2010).
- M. García-Olivo, J. M. Gutiérrez y L. J. Hernández
- Dinámica del método de Chebyshev para ecuaciones con raíces dobles
Congreso RSME 2011
Ávila (February 2011).
- S. Amat, S. Busquier y J. M. Gutiérrez
- On a family of geometric iterative methods
Congreso RSME 2011
Ávila (February 2011).
- M. García-Olivo y J. M. Gutiérrez
- El "Cálculo de las raíces de una ecuación" de P. L. Chebyshev
XI Congreso SEHCYT
Azkoitia, Guipúzcoa (September 2011).
- M. García-Olivo y J. M. Gutiérrez
- On the general convergence of Chebyshev's method
IMAC Symposium on Dynamical Systems: Trends and perspectives
Castellón (September 2011).
- J. M. Gutiérrez, Á. A. Magreñán y N. Romero
- The complex dynamics of damped Newton's method for a double root
IMAC Symposium on Dynamical Systems: Trends and perspectives
Castellón (septiembre de 2011).
- J. M. Gutiérrez, Á. A. Magreñán y J. L. Varona
- Fractal dimension of the universal Julia sets for the Chebyshev-Halley family of methods
International Conference of Numerical Analysis and Applied Mathematics 2011
Halkidiki (Grecia) (September 2011).
- J. M. Gutiérrez, Á. A. Magreñán y J. L. Varona
- A Gauss-Seidel process in iterative methods for solving non linear equations}
SIAM Conference on Applied Linear Algebra
Valencia (June 2012).
- J. M. Gutiérrez, Á. A. Magreñán y N. Romero
- On the dynamics of damped Newton's method for polynomials with a double root
18th International Conference on Difference Equations and Applications
Barcelona (July 2012).
- J. M. Gutiérrez, Á. A. Magreñán y J. L. Varona
- Dynamical Aspects of Damped Newton's Method
11th International Conference on Computational Structures Technology
Dubrovnik (Croacia) (September 2012).
- J. M. Gutiérrez, L. J. Hernández, M. Marañón y M. T. Rivas
- Un algoritmo para el cálculo de áreas de cuencas de atracción.
VII Jornadas de análisis numérico y aplicaciones
Logroño (November 2012).
- J. M. Gutiérrez y Á. A. Magreñán
- Una visión general sobre la convergencia del método de Newton amortiguado
Congreso bienal RSME 2013
Santiago de Compostela (January 2013).
- J. M. Gutiérrez
- Chebyshev's method in a nutshell
Méthodes numériques et calcul effectif
Marsella (October 2013).
- J. M. Gutiérrez
- Una visión probabil&ieacute;stica del problema de Cayley.
VIII Jornadas de análisis numérico y aplicaciones
Logroño (November 2013).
- J. M. Gutiérrez
- Una visión general del método super-Halley
I Jornadas de Análisis Numérico y sus Aplicaciones
Santo Domingo, República Dominicana (June 2014).
- J. M. Gutiérrez
- El método de Newton-Kantorovich
X Congreso Internacional Interdisciplinario de Investigación Científica
Santo Domingo, República Dominicana (June 2014).
- J. M. Gutiérrez, M. García-Olivo y Á. A. Magreñán
- Extraneous attractors for Chebyshev's method
14th International Conference on Computational and Mathematical Methods in Science and Engineering
Rota, Cádiz (July 2014).
- J. M. Gutiérrez, L. J. Hernández, Á. A. Magreñán
y M. T. Rivas
- Eficiencia inicial y cuencas de atracci—n para el mˇtodo de Newton amortiguado.
IX Jornadas de análisis numérico y aplicaciones
Logroño (November 2014).
- M. Grau-Sánchez, M. Noguera y J. M. Gutiérrez
- Multidimensional generalization of iterative methods and applications
Congreso bienal RSME 2015
Granada (February 2015).
- J. M. Gutiérrez, M. García-Olivo y Á. A. Magreñán
- A brief overview on the real dynamics of Chebyshev's method
15th International Conference on Computational and Mathematical Methods in Science and Engineering
Rota, Cádiz (July 2015).
- J. M. Gutiérrez y M. A. Hernández
- Otra construcción de la familia de Chebyshev-Halley a partir del método de Newton continuo.
X Jornadas de análisis numérico y aplicaciones
Logroño (November 2015).
- J. M. Gutiérrez y M. A. Hernández
- Some variants of continuous Newton's method.
Second Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies
Logroño (June 2016).
- J. M. Gutiérrez y Á. A. Magreñán
- Dynamical study of the Secant method.
Second Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies
Logroño (June 2016).
- J. M. Gutiérrez y M. A. Hernández
- Aceleraciones del método de Newton continuo.
Congreso bienal RSME 2017
Zaragoza (January-February 2017).
3. PhD Thesis that I have supervised