Perfil (CV) del personal docente investigador

Barrio Gil, Roberto
Departamento: Departamento de Matemática Aplicada
Área: Matemática Aplicada
Centro: Facultad de Ciencias

Research Institute: INSTITUTO UNIVERSITARIO DE MATEMÁTICAS Y APLICACIONES (IUMA)
Grupo: E24_23R: APEDIF (Aplicaciones de Ecuaciones Diferenciales)

Tramos de investigación
  • CNEAI research evaluation. 01/01/24
  • CNEAI research evaluation. 01/01/18
  • CNEAI research evaluation. 01/01/12
  • CNEAI research evaluation. 01/01/06
  • CNEAI research evaluation. 01/01/01
Categoría profesional: Cated. Universidad

Cargos
  • Director del Departamento de Matemática Aplicada
Correo electrónico: rbarrio@unizar.es
Página web: http://cody.unizar.es/people/rbarrio/
ORCID: 0000-0002-8089-343X

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Artículos

  • Barrio, Roberto; Ibáñez, Santiago; Jover-Galtier, Jorge A.; Lozano, Álvaro; Martínez, M. Ángeles; Mayora-Cebollero, Ana; Mayora-Cebollero, Carmen; Pérez, Lucía; Serrano, Sergio; Vigara, Rubén. Dynamics of excitable cells: spike-adding phenomena in action. SEMA JOURNAL. 2024. DOI: 10.1007/s40324-023-00328-2

  • Serrano, S.; Barrio, R.; Lozano, Á.; Mayora-Cebollero, A.; Vigara, R. Coupling of neurons favors the bursting behavior and the predominance of the tripod gait. CHAOS, SOLITONS AND FRACTALS. 2024. DOI: 10.1016/j.chaos.2024.114928

  • Serrano, Sergio; Barrio, Roberto; Martínez-Rubio, Álvaro; Belmonte-Beitia, Juan; Pérez-García, Víctor M. Understanding the role of B cells in CAR T-cell therapy in leukemia through a mathematical model. CHAOS. 2024. DOI: 10.1063/5.0206341

  • Barrio, Roberto; Jover-Galtier, Jorge A.; Mayora-Cebollero, Ana; Mayora-Cebollero, Carmen; Serrano, Sergio. Synaptic dependence of dynamic regimes when coupling neural populations. PHYSICAL REVIEW E. 2024. DOI: 10.1103/PhysRevE.109.014301

  • Barrio, Roberto; Ibáñez, Santiago; Pérez, Lucía. Exploring the geometry of the bifurcation sets in parameter space. SCIENTIFIC REPORTS (NATURE PUBLISHING GROUP). 2024. DOI: 10.1038/s41598-024-61574-6

  • Lozano, Álvaro; Vigara, Rubén; Mayora-Cebollero, Carmen; Barrio, Roberto. Dominant patterns in small directed bipartite networks: ubiquitous generalized tripod gait. NONLINEAR DYNAMICS. 2024. DOI: 10.1007/s11071-024-09830-2

  • Li, Ch.; Barrio, R.; Xiao, X.; Du, P.; Jiang, H.; Quan, Z.; Li, K. PACF: A precision-adjustable computational framework for solving singular values. APPLIED MATHEMATICS AND COMPUTATION. 2023. DOI: 10.1016/j.amc.2022.127611

  • Drubi, Fátima; Mayora Cebollero, Ana; Mayora Cebollero, Carmen; Ibáñez, Santiago; Jover Galtier, Jorge Alberto; Lozano, Álvaro; Pérez, Lucía; Barrio, Roberto. Connecting chaotic regions in the Coupled Brusselator System. CHAOS, SOLITONS AND FRACTALS. 2023. DOI: 10.1016/j.chaos.2023.113240

  • Barrio, R.; Jover-Galtier, J.A.; Martínez, M.A.; Pérez, L.; Serrano, S. Mathematical birth of early afterdepolarizations in a cardiomyocyte model. MATHEMATICAL BIOSCIENCES. 2023. DOI: 10.1016/j.mbs.2023.109088

  • Barrio, Roberto; Lozano, Álvaro; Mayora-Cebollero, Ana; Mayora-Cebollero, Carmen; Miguel, Antonio; Ortega, Alfonso; Serrano, Sergio; Vigara, Rubén. Deep learning for chaos detection. CHAOS. 2023. DOI: 10.1063/5.0143876

  • Nieto, A. R.; Seoane, J. M.; Barrio, R.; Sanjuan, M. A. F. A mechanism explaining the metamorphoses of KAM islands in nonhyperbolic chaotic scattering. NONLINEAR DYNAMICS. 2022. DOI: 10.1007/s11071-022-07623-z

  • Barrio, R.; Martínez, M. A.; Serrano, S.; Pueyo, E. Dynamical mechanism for generation of arrhythmogenic early afterdepolarizations in cardiac myocytes: insights from in silico electrophysiological models. PHYSICAL REVIEW E. 2022. DOI: 10.1103/PhysRevE.106.024402

  • Barrio R.; Ibáñez S.; Pérez L.; Serrano S. Classification of fold/hom and fold/Hopf spike-adding phenomena. CHAOS. 2021. DOI: 10.1063/5.0037942

  • Barrio, R.; Lozano, A.; Martínez, M.A.; Rodríguez, M.; Serrano. S. Routes to tripod gait movement in hexapods. NEUROCOMPUTING. 2021. DOI: 10.1016/j.neucom.2020.06.151

  • Serrano, Sergio; Martínez, M. Ángeles; Barrio, Roberto. Order in chaos: Structure of chaotic invariant sets of square-wave neuron models. CHAOS. 2021. DOI: 10.1063/5.0043302

  • Barrio Gil, Roberto; Martinez Carballo, María Ángeles; Pueyo Paules, Esther; Serrano Pastor, Sergio. Dynamical analysis of early afterdepolarization patterns in a biophysically detailed cardiac model. CHAOS. 2021. DOI: 10.1063/5.0055965

  • Barrio, R.; Ibáñez, S.; Pérez, L.; Serrano, S. Spike-adding structure in fold/hom bursters. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION. 2020. DOI: 10.1016/j.cnsns.2019.105100

  • Barrio, R.; Martinez, M.A.; Perez, L.; Pueyo, E. Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations. MATHEMATICS. 2020. DOI: 10.3390/math8060880

  • Barrio, R.; Coombes, S.; Desroches, M.; Fenton, F.; Luther, S.; Pueyo, E. Excitable dynamics in neural and cardiac systems. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION. 2020. DOI: 10.1016/j.cnsns.2020.105275

  • Barrio, R.; Carvalho, M.; Castro, L.; Rodrigues, A.A.P. Experimentally Accessible Orbits near a Bykov Cycle. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 2020. DOI: 10.1142/S021812742030030X

  • Barrio, R.; Wilczak, D. Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Hénon–Heiles system. NONLINEAR DYNAMICS. 2020. DOI: 10.1007/s11071-020-05930-x

  • Barrio, Roberto; Ibáñez, Santiago; Pérez, Lucía. Homoclinic organization in the Hindmarsh-Rose model: A three parameter study. CHAOS. 2020. DOI: 10.1063/1.5138919

  • Barrio, R.; Lozano, Á.; Rodríguez, M.; Serrano, S. Numerical detection of patterns in CPGs: Gait patterns in insect movement. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION. 2020. DOI: 10.1016/j.cnsns.2019.105047

  • Barrio, R. “Brainland” vs. “flatland”: How many dimensions do we need in brain dynamics?: Comment on the paper “The unreasonable effectiveness of small neural ensembles in high-dimensional brain” by Alexander N. Gorban et al.. PHYSICS OF LIFE REVIEWS. 2019. DOI: 10.1016/j.plrev.2019.02.010

  • Sun, Tao; Barrio, Roberto; Rodriguez, Marcos; Jiang, Hao. Inertial Nonconvex Alternating Minimizations for the Image Deblurring. IEEE TRANSACTIONS ON IMAGE PROCESSING. 2019. DOI: 10.1109/TIP.2019.2924339

  • Zhang X; Barrio, Roberto; Martínez, M. Ángeles; Jiang, Hao; Cheng, Lizhi. Bregman Proximal Gradient Algorithm with Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems. IEEE ACCESS. 2019. DOI: 10.1109/ACCESS.2019.2937005

  • Barrio, Roberto; Du, Peibing; Jiang, Hao; Serrano Pastor, Sergio. ORTHOPOLY: A library for accurate evaluation of series of classical orthogonal polynomials and their derivatives. COMPUTER PHYSICS COMMUNICATIONS. 2018. DOI: 10.1016/j.cpc.2018.05.004

  • Sun, T.; Barrio, R.; Jiang, H.; Cheng, L. Convergence rates of accelerated proximal gradient algorithms under independent noise. NUMERICAL ALGORITHMS. 2018. DOI: 10.1007/s11075-018-0565-4

  • Sun, T.; Barrio, R.; Cheng, L.; Jiang, H. Precompact convergence of the nonconvex Primal–Dual Hybrid Gradient algorithm. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2018. DOI: 10.1016/j.cam.2017.07.037

  • Barrio, Roberto; Ibáñez, Santiago; Pérez, Lucía. Hindmarsh–Rose model: close and far to the singular limit. PHYSICS LETTERS A. 2017. DOI: 10.1016/j.physleta.2016.12.027

  • Du, Peibing; Barrio, Roberto; Jiang, Hao; Cheng, Lizhi. Accurate quotient-difference algorithm: error analysis, improvements and applications. APPLIED MATHEMATICS AND COMPUTATION. 2017. DOI: 10.1016/j.amc.2017.04.004

  • Wilczaky, D.; Barrio, R. Systematic computer-assisted proof of branches of stable elliptic periodic orbits and surrounding invariant tori. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS. 2017. DOI: 10.1137/17M1113254

  • Sun, T.; Barrio, R.; Jiang, H.; Cheng, L. Local Linear Convergence of a Primal-Dual Algorithm for the Augmented Convex Models. JOURNAL OF SCIENTIFIC COMPUTING. 2016. DOI: 10.1007/s10915-016-0235-4

  • Lozano, A.; Rodriguez, M.; Barrio, R. Control strategies of 3-cell Central Pattern Generator via global stimuli. SCIENTIFIC REPORTS (NATURE PUBLISHING GROUP). 2016. DOI: 10.1038/srep23622

  • Wilczak, D.; Serrano, S.; Barrio, R. Coexistence and dynamical connections between hyperchaos and chaos in the 4D Rössler system: A computer-assisted proof. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS. 2016. DOI: 10.1137/15M1039201

  • Barrio,R. Theory and applications of the orthogonal Fast Lyapunov indicator (OFLI and OFLI2)methods. LECTURE NOTES IN PHYSICS. 2016. DOI: 10.1007/978-3-662-48410-4_3

  • Abad, A.; Barrio, R.; Marco-Buzunariz, M.; Rodríguez, M. Automatic implementation of the numerical Taylor series method: A Mathematica and Sage approach. APPLIED MATHEMATICS AND COMPUTATION. 2015. DOI: 10.1016/j.amc.2015.06.042

  • Rodriguez, Marcos; Blesa Moreno, Fernando; Barrio, Roberto. OpenCL parallel integration of ordinary differential equations: Applications in computational dynamics. COMPUTER PHYSICS COMMUNICATIONS. 2015. DOI: 10.1016/j.cpc.2015.02.013

  • Dena, Á.; Abad, A.; Barrio, R. Efficient computational approaches to obtain periodic orbits in Hamiltonian systems: application to the motion of a lunar orbiter. CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY. 2015. DOI: 10.1007/s10569-015-9651-2

  • Barrio, Roberto; Martínez, M. Ángeles; Serrano, Sergio; Wilczak, Daniel. When chaos meets hyperchaos: 4D Rössler model. PHYSICS LETTERS A. 2015. DOI: 10.1016/j.physleta.2015.07.035

  • Jiang, H.; Graillat, S.; Barrio, R.; Yang, C. Accurate, validated and fast evaluation of elementary symmetric functions and its application. APPLIED MATHEMATICS AND COMPUTATION. 2015. DOI: 10.1016/j.amc.2015.08.134

  • Barrio, R.; Rodríguez, M.; Serrano, S.; Shilnikov, A. Mechanism of quasi-periodic lag jitter in bursting rhythms by a neuronal network. EUROPHYSICS LETTERS. 2015. DOI: 10.1209/0295-5075/112/38002

  • Barrio, Roberto; Dena, Angeles; Tucker, Warwick. A database of rigorous and high-precision periodic orbits of the Lorenz model. COMPUTER PHYSICS COMMUNICATIONS. 2015. DOI: 10.1016/j.cpc.2015.04.007

  • Barrio, R.; Lefranc, M.; Martínez, M.A.; Serrano, S. Symbolic dynamical unfolding of spike-adding bifurcations in chaotic neuron models. EUROPHYSICS LETTERS. 2015. DOI: 10.1209/0295-5075/109/20002

  • Rodriguez Rodriguez, Marcos; Barrio Gil, Roberto. Systematic Computer Assisted Proofs of periodic orbits of Hamiltonian systems. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION. 2014. DOI: 10.1016/j.cnsns.2013.12.025

  • Barrio Gil, Roberto; Martínez Carballo, M. Ángeles; Serrano Pastor, Sergio; Shilnikov, Andrey. Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons. CHAOS. 2014. DOI: 10.1063/1.4882171

  • Blesa Moreno, Fernando; Barrio, Roberto; Serrano, Sergio. Unbounded dynamics in dissipative flows: Rössler model . CHAOS. 2014. DOI: 10.1063/1.4871712

  • Blesa Moreno, Fernando; Seoane, Jesús M.; Barrio, Roberto; Sanjuán, Miguel A. F. Effects of periodic forcing in chaotic scattering . PHYSICAL REVIEW E - STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. 2014. DOI: 10.1103/PhysRevE.89.042909

  • Xing,T.; Barrio,R.; Shilnikov,A. Symbolic quest into homoclinic chaos. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 2014. DOI: 10.1142/S0218127414400045

  • Martínez, María Ángeles; Barrio, Roberto; Serrano, Sergio. Finding Periodic Orbits in the Hindmarsh-Rose neuron model. SPRINGER PROCEEDINGS IN MATHEMATICS & STATISTICS. 2013. DOI: 10.1007/978-3-642-38830-9_18

  • Barrio, Roberto; Jiang, Hao; Serrano, Sergio. A General Condition Number for Polynomials. SIAM JOURNAL ON NUMERICAL ANALYSIS. 2013. DOI: 10.1137/120864581

  • Barrio, Roberto; Blesa, Fernando; Serrano, Sergio; Xing, Tingli; Shilnikov, Andrey. Homoclinic spirals: theory and numerics. SPRINGER PROCEEDINGS IN MATHEMATICS & STATISTICS. 2013

  • Jiang,H.; Li,H. S.; Cheng,L. Z.; Barrio,R.; Hu,C. B.; Liao,X. K. Accurate, validated and fast evaluation of bézier tensor product surfaces. RELIABLE COMPUTING. 2013

  • Jiang,H.;Graillat,S.;Barrio,R. Accurate computing elementary symmetric functions. ACM COMMUNICATIONS IN COMPUTER ALGEBRA. 2013. DOI: 10.1145/2429135.2429154

  • Serrano, Sergio; Barrio, Roberto; Dena, Angeles; Rodriguez, Marcos. Crisis curves in nonlinear business cycles. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION. 2012. DOI: 10.1016/j.cnsns.2011.06.022

  • Blesa, F.;Piasecki, S.;Dena, Á.;Barrio, R. Connecting symmetric and asymmetric families of periodic orbits in squared symmetric hamiltonians. INTERNATIONAL JOURNAL OF MODERN PHYSICS C. 2012. DOI: 10.1142/S0129183112500143

  • Barrio,R.;Rodríguez,M.;Blesa,F. Computer-assisted proof of skeletons of periodic orbits. COMPUTER PHYSICS COMMUNICATIONS. 2012. DOI: 10.1016/j.cpc.2011.09.001

  • Dena, Angeles; Rodríguez, Marcos; Serrano, Sergio; Barrio, Roberto. High-Precision Continuation of Periodic Orbits. ABSTRACT AND APPLIED ANALYSIS. 2012. DOI: 10.1155/2012/716024

  • Barrio, Roberto; Blesa, Fernando; Serrano, Sergio. Behavior patterns in multiparametric dynamical systems: Lorenz model. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 2012. DOI: 10.1142/S0218127412300194

  • Barrio, Roberto; Blesa, Fernando; Serrano, Sergio. Topological Changes in Periodicity Hubs of Dissipative Systems. PHYSICAL REVIEW LETTERS. 2012. DOI: 10.1103/PhysRevLett.108.214102

  • Bailey,D. H.;Barrio,R.;Borwein,J. M. High-precision computation: Mathematical physics and dynamics. APPLIED MATHEMATICS AND COMPUTATION. 2012. DOI: 10.1016/j.amc.2012.03.087

  • Blesa, F.;Seoane, J. M.;Barrio, R.;Sanjuán, M. A. F. To escape or not to escape, that is the question - Perturbing the Hénon-Heiles Hamiltonian. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 2012. DOI: 10.1142/S0218127412300108

  • Rodríguez, M.;Barrio, R. Reducing rounding errors and achieving Brouwer's law with Taylor Series Method. APPLIED NUMERICAL MATHEMATICS. 2012. DOI: 10.1016/j.apnum.2012.03.008

  • Abad, A.;Barrio, R.;Blesa, F.;Rodriguez, M. Algorithm 924: Tides, a taylor series integrator for differential equations. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE. 2012. DOI: 10.1145/2382585.2382590

  • Abad, Alberto; Barrio, Roberto; Dena, Angeles;. Computing periodic orbits with arbitrary precision. PHYSICAL REVIEW E - STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. 2011

  • Barrio, Roberto; Blesa, Fernando; Dena, Angeles; Serrano, Sergio. Qualitative and numerical analysis of the Rössler model: Bifurcations of equilibria. COMPUTERS & MATHEMATICS WITH APPLICATIONS. 2011. DOI: 10.1016/j.camwa.2011.09.064

  • Blesa Moreno, Fernando; Rodríguez, Marcos; Abad, Alberto; Barrio, Roberto. TIDES: A free software based on the Taylor series method. MONOGRAFÍAS DE LA ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS, QUÍMICAS Y NATURALES DE ZARAGOZA. 2011

  • Blesa Moreno, Fernando; Barrio, Roberto; Piasecki, Slawek. Symmetry breaking bifurcations in a D4 symmetric Hamiltonian system PUBLICACIONES DEL SEMINARIO MATEMÁTICO GARCÍA DE GALDEANO. 2011

  • Li, H.;Jiang, H.;Barrio, R.;Liao, X.;Cheng, L. ;Su, F. Incremental manifold learning by spectral embedding methods. PATTERN RECOGNITION LETTERS. 2011

  • Barrio, R.;Rodríguez, M.;Abad, A. ;Blesa, F. Breaking the limits: The Taylor series method. APPLIED MATHEMATICS AND COMPUTATION. 2011. DOI: 10.1016/j.amc.2011.02.080

  • Barrio,R.;Blesa,F.;Serrano,S.;Shilnikov,A. Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci. PHYSICAL REVIEW E - STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. 2011. DOI: 10.1103/PhysRevE.84.035201

  • Jiang,H.;Barrio,R.;Li,H.;Liao,X.;Cheng,L.;Su,F. Accurate evaluation of a polynomial in Chebyshev form. APPLIED MATHEMATICS AND COMPUTATION. 2011. DOI: 10.1016/j.amc.2011.04.054

  • Jiang, H.; Barrio, R.; Liao, X.; Cheng, L. Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form. APPLIED NUMERICAL MATHEMATICS. 2011. DOI: 10.1016/j.apnum.2011.07.009

  • Abad, Alberto; Barrio, Roberto; Blesa, Fernando; Rodriguez, Marcos;. TIDES tutorial: Integrating ODEs by using the Taylor Series Method. MONOGRAFÍAS DE LA ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS, QUÍMICAS Y NATURALES DE ZARAGOZA. 2011

  • Barrio, Roberto; Rodriguez, Marcos; Abad, Alberto; Serrano, Sergio. Uncertainty propagation or box propagation. MATHEMATICAL AND COMPUTER MODELLING. 2011. DOI: 10.1016/j.mcm.2011.06.036

  • Abad, A.; Barrio, R.; Dena, A. Computing periodic orbits with arbitrary precision. PHYSICAL REVIEW E - STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. 2011. DOI: 10.1103/PhysRevE.84.016701

  • Barrio, Roberto; Serrano, Sergio. Modificaciones del método de Variación de los Parámetros. Aplicaciones en Astrodinámica. REVISTA DE LA ACADEMIA DE CIENCIAS EXACTAS, FÍSICO-QUÍMICAS Y NATURALES DE ZARAGOZA. 2010

  • Barrio, R.;Blesa, F. ;Serrano, S. Bifurcations and chaos in hamiltonian systems. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 2010

  • Barrio, R.;Peña, J. M. ;Sauer, T. Three term recurrence for the evaluation of multivariate orthogonal polynomials. JOURNAL OF APPROXIMATION THEORY. 2010

  • Barrio, Roberto; Serrano, Sergio. Sobre el método de variación de los parámetros. BOLETÍN ROA. 2009

  • Barrio, R.;Borczyk,W.;Breiter,S. Spurious Structures in Chaos Indicators Maps. CHAOS, SOLITONS AND FRACTALS. 2009

  • Barrio, R.;Blesa,F. Systematic Search of Symmetric Periodic Orbits in 2DOF Hamiltonian Systems. CHAOS, SOLITONS AND FRACTALS. 2009

  • Barrio, R.;Blesa,F.;Serrano,S. Bifurcations and Safe Regions in Open Hamiltonians. NEW JOURNAL OF PHYSICS. 2009

  • Barrio, R.;Blesa,F.;Serrano,S. Qualitative Analysis of the Rossler Equations: Bifurcations of Limit Cycles and Chaotic Attractors. PHYSICA D-NONLINEAR PHENOMENA. 2009

  • Barrio, R.;Blesa,F.;Serrano,S. Periodic, Escape and Chaotic Orbits in the Copenhagen and the (n+1)-Body Ring Problems. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION. 2009

  • Barrio, R.;Serrano,S. Bounds for the Chaotic Region in the Lorenz Model. PHYSICA D-NONLINEAR PHENOMENA. 2009

  • Barrio, R.;Blesa,F.;Serrano,S. Qualitative Analysis of the (N+1)-Body Ring Problem. CHAOS, SOLITONS AND FRACTALS. 2008

  • Barrio, R.;Serrano,S. Performance of Perturbation Methods on Orbit Prediction. MATHEMATICAL AND COMPUTER MODELLING. 2008

  • Barrio, R. ; Blesa, F. ; Serrano, S. Fractal Structures in the Hénon-Heiles Hamiltonian. EUROPHYSICS LETTERS. 2008

  • Barrio, Roberto; Blesa, Fernando; Serrano, Sergio. Is there chaos in Copenhagen problem?. MONOGRAFÍAS DE LA ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS, QUÍMICAS Y NATURALES DE ZARAGOZA. 2007

  • Barrio, R.;Blesa,F.;Serrano,S. ¿Hay Caos En El Problema De Copenague?. MONOGRAFÍAS DE LA ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS, QUÍMICAS Y NATURALES DE ZARAGOZA. 2007

  • Barrio, R.;Serrano,S. A Three-Parametric Study of the Lorenz Model. PHYSICA D-NONLINEAR PHENOMENA. 2007

  • Barrio,R.;Serrano,S. Modifications of the method of variation of parameters. COMPUTERS & MATHEMATICS WITH APPLICATIONS. 2006

  • Barrio, R. ; Blesa, F. ; Elipe, A. On the use of chaos indicators in rigid-body dynamics. JOURNAL OF THE ASTRONAUTICAL SCIENCES. 2006

  • Barrio,R. Painting chaos: A gallery of sensitivity plots of classical problems. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 2006

  • Barrio,R. Sensitivity analysis of ODEs. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 2006

  • Barrio, Roberto. Performance of the Taylor series method for ODEs/DAEs. APPLIED MATHEMATICS AND COMPUTATION. 2005

  • Barrio, R.; Serrano, S. Generation and Evaluation of Orthogonal Polynomials in Discrete Sobolev Spaces II: Numerical Stability. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2005

  • Barrio, R.;Melendo, B.;Serrano, S. Generation and Evaluation of Orthogonal Polynomials in Discrete Sobolev Spaces I: Algorithms. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2005

  • Barrio, R.;Blesa, F.;Lara, M. Vsvo Formulation of the Taylor Method for the Numerical Solution of Odes. COMPUTERS & MATHEMATICS WITH APPLICATIONS. 2005

  • Barrio, R.;Peña, J. M. Evaluation of the Derivative of a Polynomial in Bernstein Form. APPLIED MATHEMATICS AND COMPUTATION. 2005

  • Barrio, Roberto. Sensitivity tools vs. Poincare sections. CHAOS, SOLITONS AND FRACTALS. 2005

  • Barrio, Roberto;Peña, Juan Manuel. Basis conversions among univariate polynomial representations. COMPTES RENDUS MATHEMATIQUE. 2004

  • Barrio, R.;Serrano, S. High-Order Recurrences Satisfied by Classical Orthogonal Polynomials. APPLIED MATHEMATICS LETTERS. 2004

  • Barrio, Roberto;Delgado, Jorge. Trayectorias de los ceros de los polinomios ortogonales de Sobolev-Gegenbauer. REVISTA DE LA ACADEMIA DE CIENCIAS EXACTAS, FÍSICO-QUÍMICAS Y NATURALES DE ZARAGOZA. 2004

  • Barrio, R. Algorithms for the Integration and Derivation of Chebyshev Series. APPLIED MATHEMATICS AND COMPUTATION. 2004

  • Barrio, R. A Unified Rounding Error Bound for Polynomial Evaluation. ADVANCES IN COMPUTATIONAL MATHEMATICS. 2003

  • Barrio, R.;Palacian, J. High-Order Averaging of Eccentric Artificial Satellites Perturbed by the Earth's Potential and Air-Drag Terms. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. 2003

  • Barrio, R.;Blesa, F.;Lara, M. Solución numérica de alta precisión de ecuaciones diferenciales ordinarias con métodos de Taylor de orden superior en paralelo. MEMORIAS DE LA ACADEMIA DE CIENCIAS EXACTAS, FÍSICO- QUÍMICAS Y NATURALES DE ZARAGOZA. 2003

  • Barrio, R.;Yalamov, P. Stability of Parallel Algorithms for Polynomial Evaluation. COMPUTERS & MATHEMATICS WITH APPLICATIONS. 2003

  • Barrio, R.;Melendo, B.;Serrano, S. On the Numerical Evaluation of Linear Recurrences. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2003

  • Barrio, R. Compression of Almost-Periodic Data. APPLIED MATHEMATICS AND COMPUTATION. 2003

  • Barrio, R.;Peña, J.M. Numerical evaluation of the pth derivative of Jacobi series. APPLIED NUMERICAL MATHEMATICS. 2002

  • Barrio, Roberto. Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 2002

  • Barrio, R; Elipe, A. Compression of satellite data. REVISTA MATEMATICA COMPLUTENSE. 2002

  • Barrio, R. Stability of parallel algorithms to evaluate Chebyshev series. COMPUTERS & MATHEMATICS WITH APPLICATIONS. 2001

  • Barrio, R. Parallel Algorithms to Evaluate Orthogonal Polynomial Series. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 2000

  • Barrio, R. Sobre la evaluación numérica de polinomios ortogonales. MEMORIAS DE LA ACADEMIA DE CIENCIAS EXACTAS, FÍSICO- QUÍMICAS Y NATURALES DE ZARAGOZA. 2000

  • Barrio, R.;Sabadell, J. Parallel evaluation of Chebyshev and trigonometric series. COMPUTERS & MATHEMATICS WITH APPLICATIONS. 1999

  • Barrio, R.;Sabadell, J. A parallel algorithm to evaluate Chebyshev series on a message passing environment. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 1999

  • Barrio, R. Characterization of low degree A-stable symmetric RK collocation methods. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. 1999

  • Barrio, R. On the A-stability of Runge-Kutta collocation methods based on orthogonal polynomials. SIAM JOURNAL ON NUMERICAL ANALYSIS. 1999

  • Barrio, R.;Palacios, M.;Elipe, A. Chebyshev collocation methods for fast orbit determination. APPLIED MATHEMATICS AND COMPUTATION. 1999

  • Barrio, R. Análisis matricial de la estabilidad del algoritmo de Clenshaw. EXTRACTA MATHEMATICAE. 1998

  • Barrio, R.;Palacian, J. Lie transforms for ordinary differential equations: Taking advantage of the Hamiltonian form of terms of the perturbation. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING. 1997

  • Barrio, R. Coeficientes minimax de Chebyshev del dilogaritmo real. REVISTA DE LA ACADEMIA DE CIENCIAS EXACTAS, FÍSICO-QUÍMICAS Y NATURALES DE ZARAGOZA. 1997

Libros

  • Roberto Barrio Gil ; [directores, Antonio Elipe Sánchez, Manuel Pedro Palacios Latasa]. Polinomios de Chebyshev, algoritmos y aplicaciones en la determinación y compresión de órbitas. 1997

  • Roberto Barrio, Carlos López, Eduardo Martínez. Cálculo vectorial: prácticas con Mathematica y Maple. 1997



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