Roberto Barrio

Full Professor in Applied Mathematics

Department of Applied Mathematics
Universidad de Zaragoza, Spain
Edificio de Matemáticas, planta tercera.
c/ Pedro Cerbuna 12, 50009-Zaragoza, SPAIN.

rbarrio@unizar.es

+34 976762480

Editorial boards

Publications

  1. A. Mayora-Cebollero, J. A. Jover-Galtier, F. Drubi, S. Ibañez, Á. Lozano Rojo, C. Mayora-Cebollero and R. Barrio. Almost synchronization phenomena in the two and three coupled Brusselator systems , Physica D: Nonlinear Phenomena 472 (2025) 134457. doi 10.1016/j.physd.2024.134457
  2. Á. Lozano Rojo, R. Vigara Benito, R. Barrio and C. Mayora-Cebollero. Dominant patterns in small directed bipartite networks: ubiquitous generalized tripod gait , Nonlinear Dynamics 112 (2024) 15549–15565. doi 10.1007/s11071-024-09830-2
  3. C. Mayora-Cebollero, A. Mayora-Cebollero, Á. Lozano Rojo and R. Barrio. Full Lyapunov Exponents spectrum with Deep Learning from single-variable time series , arXiv (2024).
  4. F. Drubi, A. Mayora-Cebollero, C. Mayora-Cebollero, S. Ibáñez, J. A. Jover-Galtier, Á. Lozano Rojo, L. Pérez and R. Barrio. Connecting chaotic regions in the Coupled Brusselator System, Chaos, Solitons & Fractals 169 (2023) 113240. doi 10.1016/j.chaos.2023.113240
  5. R. Barrio, S. Ibañez, J. A. Jover-Galtier, Á. Lozano Rojo, M. Á. Martínez, A. Mayora-Cebollero, C. Mayora-Cebollero, L. Pérez, S. Serrano and R. Vigara Benito. Dynamics of excitable cells: spike-adding phenomena in action, SeMA Journal (2023). doi 10.1007/s40324-023-00328-2
  6. R. Barrio, Á. Lozano Rojo, A. Mayora-Cebollero, C. Mayora-Cebollero, A. Miguel, A. Ortega, S. Serrano and R. Vigara Benito. Deep Learning for Chaos Detection, Chaos 33 7 (2023) 30310. doi 10.1063/5.0143876
  7. R. Barrio, Á. Lozano Rojo, M. Martínez, M. Rodríguez and S. Serrano. Routes to tripod gait movement in hexapods, Neurocomputing 461 (2021) 679–695. doi 10.1016/j.neucom.2020.06.151
  8. R. Barrio, S Coombes, M Desroches, F Fenton, S Luther and E Pueyo. Excitable dynamics in neural and cardiac systems, Communications in Nonlinear Science and Numerical Simulation 86 (2020) 105275.
  9. R. Barrio, S. Ibáñez and L. Pérez. Homoclinic organization in the Hindmarsh–Rose model: A three parameter study, Chaos: An Interdisciplinary Journal of Nonlinear Science 30 5 (2020) 22106.
  10. R. Barrio, M. Á. Martínez, L. Pérez and E Pueyo. Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations, Mathematics 8 6 (2020) 880.
  11. R. Barrio and D Wilczak. Distribution of stable islands within chaotic areas in the non-hyperbolic and hyperbolic regimes in the Hénon–Heiles system, Nonlinear Dynamics 102 1 (2020) 403–416.
  12. MP de Carvalho, R. Barrio, A. Rodrigues and ML Castro. Experimentally accessible orbits near a Bykov cycle, International Journal of Bifurcation and Chaos 30 10 (2020) 2030030.
  13. R. Barrio, Á. Lozano, M. Rodríguez and S. Serrano. Numerical detection of patterns in CPGs: Gait patterns in insect movement, Communications in Nonlinear Science and Numerical Simulation 82 (2020) 105047. doi 10.1016/j.cnsns.2019.105047
  14. R. Barrio, S. Ibáñez, L. Pérez and S. Serrano. Spike-adding structure in fold/hom bursters, Communications in Nonlinear Science and Numerical Simulation 83 (2020) 105100. doi 10.1016/j.cnsns.2019.105100
  15. R. Barrio, M. Á. Martínez, L. Pérez and E Pueyo. Bifurcations and Slow-Fast Analysis in a Cardiac Cell Model for Investigation of Early Afterdepolarizations, Mathematics 8 6 (2020) 880. doi 10.3390/math8060880
  16. T Sun, R. Barrio, H Jiang and L Cheng. Convergence rates of accelerated proximal gradient algorithms under independent noise, Numerical Algorithms 81 2 (2019) 631–654.
  17. T Sun, R. Barrio, M. Rodríguez and H Jiang. Inertial nonconvex alternating minimizations for the image deblurring, IEEE Transactions on Image Processing 28 12 (2019) 6211–6224.
  18. R. Barrio. “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 29 (2019) 108–110.
  19. X Zhang, R. Barrio, M. Á. Martínez, H Jiang and L Cheng. Bregman proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth minimization problems, IEEE Access 7 (2019) 126515–126529.
  20. T Sun, R. Barrio, M. Rodríguez and H Jiang. Inertial nonconvex alternating minimizations for the image deblurring, IEEE Transactions on Image Processing 28 12 (2019) 6211–6224.
  21. T. Sun, R. Barrio, L. Cheng and H. Jiang. Precompact convergence of the nonconvex Primal–Dual Hybrid Gradient algorithm, Journal of Computational and Applied Mathematics 330 (2018) 15–27.
  22. R. Barrio, P Du, H Jiang and S. Serrano. ORTHOPOLY: A library for accurate evaluation of series of classical orthogonal polynomials and their derivatives, Computer Physics Communications 231 2 (2018) 146–162.
  23. D. Wilczak and R. Barrio. Systematic computer-assisted proof of branches of stable elliptic periodic orbits and surrounding invariant tori, SIAM Journal on Applied Dynamical Systems 16 3 (2017) 1618–1649.
  24. R. Barrio, S. Ibáñez and L. Pérez. Hindmarsh–Rose model: Close and far to the singular limit, Physics Letters A 381 6 (2017) 597–603.
  25. P. Du, R. Barrio, H. Jiang and L. Cheng. Accurate Quotient-Difference algorithm: error analysis, improvements and applications, Applied Mathematics and Computation 309 (2017) 245–271.
  26. T. Sun, R. Barrio, H. Jiang and L. Cheng. Local linear convergence of a primal-dual algorithm for the augmented convex models, Journal of Scientific Computing 69 3 (2016) 1301–1315.
  27. R. Barrio. Theory and Applications of the Orthogonal Fast Lyapunov Indicator (OFLI and OFLI2) Methods, In Chaos Detection and Predictability, 2016.
  28. D. Wilczak, S. Serrano and R. Barrio. Coexistence and Dynamical Connections between Hyperchaos and Chaos in the 4D Rössler System: A Computer-Assisted Proof, SIAM Journal on Applied Dynamical Systems 15 1 (2016) 356–390. doi 10.1137/15M1039201
  29. H. Jiang, S. Graillat, R. Barrio and C. Yang. Accurate, validated and fast evaluation of elementary symmetric functions and its application, Applied Mathematics and Computation 273 (2016) 1160–1178.
  30. Á. Dena, A. Abad and R. Barrio. Efficient computational approaches to obtain periodic orbits in Hamiltonian systems: application to the motion of a lunar orbiter, Celestial Mechanics and Dynamical Astronomy 124 1 (2016) 51–71.
  31. Á. Lozano Rojo, M. Rodríguez Rodríguez and R. Barrio. Control strategies of 3-cell Central Pattern Generator via global stimuli, Scientific Reports 6 (2016) 23622. doi 10.1038/srep23622
  32. R. Barrio. Taylor Series Methods, Encyclopedia of Applied and Computational Mathematics (2015) 1465–1470.
  33. R. Barrio, M. Rodríguez, S. Serrano and A. Shilnikov. Mechanism of quasi-periodic lag jitter in bursting rhythms by a neuronal network, EPL (Europhysics Letters) 112 3 (2015) 38002. doi 10.1209/0295-5075/112/38002
  34. R. Barrio, M. Á. Martínez, S. Serrano and D. Wilczak. When chaos meets hyperchaos: 4D Rössler model, Physics Letters A 379 38 (2015) 2300–2305.
  35. A. Abad, R. Barrio, M Marco-Buzunariz and M. Rodríguez. Automatic implementation of the numerical Taylor series method: a Mathematica and Sage approach, Applied Mathematics and Computation 268 (2015) 227–245.
  36. R. Barrio, Á. Dena and W. Tucker. A database of rigorous and high-precision periodic orbits of the Lorenz model, Computer Physics Communications 194 (2015) 76–83.
  37. M. Rodríguez, F. Blesa and R. Barrio. OpenCL parallel integration of ordinary differential equations: Applications in computational dynamics, Computer Physics Communications 192 (2015) 228–236.
  38. R. Barrio, M. Lefranc, M. Á. Martínez and S. Serrano. Symbolic dynamical unfolding of spike-adding bifurcations in chaotic neuron models, EPL (Europhysics Letters) 109 2 (2015) 20002.
  39. R. Barrio, M. Rodríguez, S. Serrano and A. Shilnikov. Mechanism of quasi-periodic lag jitter in bursting rhythms by a neuronal network, EPL (Europhysics Letters) 112 3 (2015) 38002.
  40. A. Abad, R. Barrio, M. Á. Marco-Buzunariz and M. Rodríguez. Automatic implementation of the numerical Taylor series method: a Mathematica and Sage approach, Applied Mathematics and Computation 268 (2015) 227–245.
  41. M. Rodríguez, F. Blesa and R. Barrio. OpenCL parallel integration of ordinary differential equations: Applications in computational dynamics, Computer Physics Communications 192 (2015) 228–236.
  42. T. Xing, R. Barrio and A. Shilnikov. Symbolic quest into homoclinic chaos, International Journal of Bifurcation and Chaos 24 8 (2014) 1440004.
  43. R. Barrio, M. Á. Martínez, S. Serrano and A. Shilnikov. Macro-and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons, Chaos: An Interdisciplinary Journal of Nonlinear Science 24 2 (2014) 023128.
  44. R. Barrio, F. Blesa and S. Serrano. Unbounded dynamics in dissipative flows: Rössler model, Chaos: An Interdisciplinary Journal of Nonlinear Science 24 2 (2014) 024407.
  45. F. Blesa, J. M Seoane, R. Barrio and M. AF Sanjuán. Effects of periodic forcing in chaotic scattering, Physical Review E 89 4 (2014) 042909.
  46. R. Barrio and M. Rodríguez. Systematic Computer Assisted Proofs of periodic orbits of Hamiltonian systems, Communications in Nonlinear Science and Numerical Simulation 19 8 (2014) 2660–2675.
  47. T. Xing, J. Wojcik, R. Barrio and A. Shilnikov. Symbolic toolkit for chaos explorations, In International Conference on Theory and Application in Nonlinear Dynamics (ICAND 2012), 2014.
  48. R. Barrio and M. Rodríguez. Systematic Computer Assisted Proofs of periodic orbits of Hamiltonian systems, Communications in Nonlinear Science and Numerical Simulation 19 8 (2014) 2660–2675.
  49. R. Barrio, F. Blesa, S. Serrano and A. Shilnikov. Homoclinic Spirals: Theory and Numerics, In Progress and Challenges in Dynamical Systems, 2013.
  50. M. Á. Martínez, R. Barrio and S. Serrano. Finding periodic orbits in the Hindmarsh-Rose neuron model, In Progress and Challenges in Dynamical Systems, 2013.
  51. H. Jiang, S. Graillat and R. Barrio. Accurate and fast evaluation of elementary symmetric functions, In 21st IEEE Symposium on Computer Arithmetic (ARITH), 2013.
  52. H. Jiang, H. Li, L. Cheng, R. Barrio, C. Hu and X. Liao. Accurate, Validated and Fast Evaluation of Bézier Tensor Product Surfaces., Reliable Computing 18 (2013) 55–72.
  53. R. Barrio, H. Jiang and S. Serrano. A general condition number for polynomials, SIAM Journal on Numerical Analysis 51 2 (2013) 1280–1294. doi 10.1137/120864581
  54. H. Jiang, S. Graillat and R. Barrio. Accurate computing elementary symmetric functions, ACM Communications in Computer Algebra 46 3/4 (2013) 102–103.
  55. A. Shilnikov, L. Shilnikov and R. Barrio. Symbolic dynamics and spiral structures due to the saddle-focus bifurcations, In Chaos, CNN, Memristors and Beyond: A Festschrift for Leon Chua. Edited by Adamatzky Andrew et al., 2013.
  56. R. Barrio and A. Elipe. Dynamics and Astrometry of Natural and Artificial Celestial Bodies, In Proceedings of IAU Colloquium 165 Poznań, Poland July 1–5, 1996, 2012.
  57. S. Piasecki, R. Barrio and F. Blesa. Symmetry breaking bifurcations in a D4 symmetric Hamiltonian system, Monografías Matemáticas García de Galdeano 37 (2012) 189–196.
  58. D. H Bailey, R. Barrio and J. M Borwein. High-precision computation: Mathematical physics and dynamics, Applied Mathematics and Computation 218 20 (2012) 10106–10121.
  59. F. Blesa, J. M Seoane, R. Barrio and M. AF Sanjuan. To escape or not to escape, that is the question—perturbing the Hénon–Heiles Hamiltonian, International Journal of Bifurcation and Chaos 22 6 (2012) 1230010.
  60. R. Barrio, F. Blesa and S. Serrano. Behavior patterns in multiparametric dynamical systems: Lorenz model, International Journal of Bifurcation and Chaos 22 6 (2012) 1230019.
  61. R. Barrio, F. Blesa and S. Serrano. Topological changes in periodicity hubs of dissipative systems, Physical review letters 108 21 (2012) 214102. doi 10.1103/PhysRevLett.108.214102
  62. Á. Dena, M. Rodríguez, S. Serrano and R. Barrio. High-precision continuation of periodic orbits, Abstract and Applied Analysis 2012 (2012) 716024. doi 10.1155/2012/716024
  63. R. Barrio, A. Shilnikov and L. Shilnikov. Kneadings, symbolic dynamics and painting Lorenz chaos, International Journal of Bifurcation and Chaos 22 4 (2012) 1230016. doi 10.1142/S0218127412300169
  64. M. Rodríguez and R. Barrio. Reducing rounding errors and achieving Brouwerʼs law with Taylor Series Method, Applied Numerical Mathematics 62 8 (2012) 1014–1024. doi 10.1016/j.apnum.2012.03.008
  65. F. Blesa, S. Piasecki, Á. Dena and R. Barrio. Connecting symmetric and asymmetric families of periodic orbits in squared symmetric Hamiltonians, International Journal of Modern Physics C 23 2 (2012) 1250014.
  66. R. Barrio, M. Rodríguez and F. Blesa. Computer-assisted proof of skeletons of periodic orbits, Computer Physics Communications 183 1 (2012) 80–85.
  67. S. Serrano, R. Barrio, A Dena and M Rodríguez. Crisis curves in nonlinear business cycles, Communications in nonlinear Science and Numerical simulation 17 2 (2012) 788–794.
  68. R. Barrio, M. Rodríguez and F. Blesa. Computer-assisted proof of skeletons of periodic orbits, Computer Physics Communications 183 1 (2012) 80–85.
  69. S. Serrano, R. Barrio, Á. Dena and M. Rodríguez. Crisis curves in nonlinear business cycles, Communications in nonlinear Science and Numerical simulation 17 2 (2012) 788–794.
  70. A. Abad, R. Barrio, F. Blesa and M. Rodríguez. Algorithm 924: TIDES, a Taylor series integrator for differential equations, ACM Transactions on Mathematical Software (TOMS) 39 1 (2012) 5. doi 10.1145/2382585.2382590
  71. H. Jiang, R. Barrio, X. Liao and L. Cheng. Accurate evaluation algorithm for bivariate polynomial in Bernstein–Bézier form, Applied Numerical Mathematics 61 11 (2011) 1147–1160.
  72. R. Barrio, M. Rodríguez, A. Abad and S. Serrano. Uncertainty propagation or box propagation, Mathematical and Computer Modelling 54 11 (2011) 2602–2615. doi 10.1016/j.mcm.2011.06.036
  73. H. Li, H. Jiang, R. Barrio, X. Liao, L. Cheng and F. Su. Incremental manifold learning by spectral embedding methods, Pattern Recognition Letters 32 10 (2011) 1447–1455.
  74. R. Barrio, F. Blesa, A. Dena and S. Serrano. Qualitative and numerical analysis of the Rössler model: Bifurcations of equilibria, Computers & Mathematics with Applications 62 11 (2011) 4140–4150.
  75. A. Abad, R. Barrio and A. Dena. Computing periodic orbits with arbitrary precision, Physical review E 84 1 (2011) 016701. doi 10.1103/PhysRevE.84.016701
  76. R. Barrio, F. Blesa, S. Serrano and A. Shilnikov. Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci, Physical Review E 84 3 (2011) 035201.
  77. H. Jiang, R. Barrio, H. Li, X. Liao, L. Cheng and F. Su. Accurate evaluation of a polynomial in Chebyshev form, Applied Mathematics and Computation 217 23 (2011) 9702–9716.
  78. R. Barrio and A. Shilnikov. Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model, The Journal of Mathematical Neuroscience 1 (2011) 6. doi 10.1186/2190-8567-1-6
  79. R. Barrio, M. Rodríguez, A. Abad and F. Blesa. Breaking the limits: the Taylor series method, Applied mathematics and computation 217 20 (2011) 7940–7954. doi 10.1016/j.amc.2011.02.080
  80. R. Barrio, F. Blesa and S. Serrano. Bifurcations and chaos in Hamiltonian systems, International Journal of Bifurcation and Chaos 20 5 (2010) 1293–1319. doi 10.1142/S0218127410026496
  81. R. Barrio, J. M. Peña and T. Sauer. Three term recurrence for the evaluation of multivariate orthogonal polynomials, Journal of Approximation Theory 162 2 (2010) 407–420.
  82. R. Barrio and S. Serrano. Sobre el método de Variación de los Parámetros, Boletín ROA 1 (2009) 25–31.
  83. R. Barrio, F. Blesa and S. Serrano. Periodic, escape and chaotic orbits in the Copenhagen and the (n+1)-body ring problems, Communications in Nonlinear Science and Numerical Simulation 14 5 (2009) 2229–2238.
  84. R. Barrio and S. Serrano. Bounds for the chaotic region in the Lorenz model, Physica D: Nonlinear Phenomena 238 16 (2009) 1615–1624.
  85. R. Barrio, F. Blesa and S. Serrano. Bifurcations and safe regions in open Hamiltonians, New Journal of Physics 11 5 (2009) 053004.
  86. R. Barrio, F. Blesa and S. Serrano. Qualitative analysis of the Rössler equations: Bifurcations of limit cycles and chaotic attractors, Physica D: Nonlinear Phenomena 238 13 (2009) 1087–1100. doi j.physd.2009.03.010
  87. R. Barrio, W. Borczyk and S Breiter. Spurious structures in chaos indicators maps, Chaos, Solitons & Fractals 40 4 (2009) 1697–1714.
  88. R. Barrio and F. Blesa. Systematic search of symmetric periodic orbits in 2DOF Hamiltonian systems, Chaos, Solitons & Fractals 41 2 (2009) 560–582.
  89. R. Barrio and S. Serrano. Performance of perturbation methods on orbit prediction, Mathematical and Computer Modelling 48 3 (2008) 594–600.
  90. R. Barrio, F. Blesa and S. Serrano. Fractal structures in the Henon-Heiles hamiltonian, EPL (Europhysics Letters) 82 1 (2008) 10003.
  91. R. Barrio, F. Blesa and S. Serrano. Qualitative analysis of the (N+1)-body ring problem, Chaos, Solitons & Fractals 36 4 (2008) 1067–1088.
  92. R. Barrio, F. Blesa and S. Serrano. Is there chaos in Copenhagen problem?, Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza 30 (2007) 51–65.
  93. R. Barrio and S. Serrano. A three-parametric study of the Lorenz model, Physica D: Nonlinear Phenomena 229 1 (2007) 43–51.
  94. R. Barrio. Painting chaos: OFLI2TT, Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza 28 (2006) 85–94.
  95. R. Barrio, F. Blesa and A Elipe. On the use of chaos indicators in rigid-body motion, The Journal of the Astronautical Sciences 54 3 (2006) 359–368.
  96. R. Barrio and S. Serrano. Modifications of the method of variation of parameters, Computers & Mathematics with Applications 51 3-4 (2006) 451–466.
  97. R. Barrio. Painting chaos: a gallery of sensitivity plots of classical problems, International Journal of Bifurcation and Chaos 16 10 (2006) 2777–2798.
  98. R. Barrio. Sensitivity analysis of ODEs/DAEs using the Taylor series method, SIAM Journal on Scientific Computing 27 6 (2006) 1929–1947. doi 10.1137/030601892
  99. R. Barrio and S. Serrano. Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces II: numerical stability, Journal of computational and applied mathematics 181 2 (2005) 299–320.
  100. R. Barrio and J. M. Peña. Evaluation of the derivative of a polynomial in Bernstein form, Applied mathematics and computation 167 1 (2005) 125–142.
  101. R. Barrio, B Melendo and S. Serrano. Generation and evaluation of orthogonal polynomials in discrete Sobolev spaces I: algorithms, Journal of computational and applied mathematics 181 2 (2005) 280–298.
  102. R. Barrio. Sensitivity tools vs. Poincaré sections, Chaos, Solitons & Fractals 25 3 (2005) 711–726.
  103. R. Barrio. Performance of the Taylor series method for ODEs/DAEs, Applied Mathematics and Computation 163 2 (2005) 525–545. doi 10.1016/j.amc.2004.02.015
  104. R. Barrio, F. Blesa and M Lara. VSVO formulation of the Taylor method for the numerical solution of ODEs, Computers & mathematics with Applications 50 1 (2005) 93–111. doi 10.1016/j.camwa.2005.02.010
  105. J. Delgado and R. Barrio. Trajectories of zeros of Sobolev-Gegengauer orthogonal polynomials, Revista de la Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza 59 (2004) 101–108.
  106. R. Barrio and S. Serrano. High-order recurrences satisfied by classical orthogonal polynomials, Applied mathematics letters 17 6 (2004) 667–670.
  107. R. Barrio. Algorithms for the integration and derivation of Chebyshev series, Applied mathematics and computation 150 3 (2004) 707–717.
  108. R. Barrio and J. M. Peña. Basis conversions among univariate polynomial representations, Comptes Rendus Mathematique 339 4 (2004) 293–298.
  109. R. Barrio, B. Melendo and S. Serrano. Some remarks on the evaluation of linear recurrences, In VII Jornadas Zaragoza-Pau de Matemática Aplicada y estadística: Jaca (Huesca), 17-18 de septiembre de 2001, 2003.
  110. R. Barrio, F. Blesa and M. Lara Coira. High-precision numerical solution of ODE with high-order Taylor methods in parallel, Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza 22 (2003) 67–74.
  111. R. Barrio and P Yalamov. Stability of parallel algorithms for polynomial evaluation, Computers & Mathematics with Applications 46 5-6 (2003) 769–781.
  112. R. Barrio. Compression of almost-periodic data, Applied mathematics and computation 134 2 (2003) 431–444.
  113. R. Barrio and J. Palacián. High-order averaging of eccentric artificial satellites perturbed by the Earth’ potential and air-drag terms, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 459 (2003) 1517–1534.
  114. R. Barrio. A unified rounding error bound for polynomial evaluation, Advances in Computational Mathematics 19 4 (2003) 385–399.
  115. R. Barrio, B Melendo and S. Serrano. On the numerical evaluation of linear recurrences, Journal of computational and applied mathematics 150 1 (2003) 71–86.
  116. R. Barrio and A. Elipe. Compression of Satellite Data, Revista Matemática Complutense 15 1 (2002) 85–100.
  117. R. Barrio. Rounding error bounds for the Clenshaw and Forsythe algorithms for the evaluation of orthogonal polynomial series, Journal of computational and applied mathematics 138 2 (2002) 185–204.
  118. R. Barrio and JM Peña. Numerical evaluation of the p-th derivative of Jacobi series, Applied numerical mathematics 43 4 (2002) 335–357.
  119. R. Barrio and P. Yalamov. Stability analysis of parallel evaluation of finite series of orthogonal polynomials, In International Conference on Numerical Analysis and Its Applications, 2000.
  120. R. Barrio. Construction of seminumerical schemes: Application to the artificial satellite problem, In International Conference on Numerical Analysis and Its Applications, 2000.
  121. R. Barrio. Parallel algorithms to evaluate orthogonal polynomial series, SIAM Journal on Scientific Computing 21 6 (2000) 2225–2239.
  122. R. Barrio. Characterization of low degree A-stable symmetric RK collocation methods, Journal of computational and applied mathematics 111 1 (1999) 1–11.
  123. R. Barrio and J Sabadell. Parallel evaluation of Chebyshev and trigonometric series, Computers & Mathematics with Applications 38 11-12 (1999) 99–106.
  124. R. Barrio. On the A-Stability of Runge–Kutta Collocation Methods Based on Orthogonal Polynomials, SIAM journal on numerical analysis 36 4 (1999) 1291–1303.
  125. R. Barrio, M. Palacios and A. Elipe. Chebyshev collocation methods for fast orbit determination, Applied Mathematics and Computation 99 2-3 (1999) 195–207.
  126. R. Barrio. A matrix analysis of the stability of the Clenshaw algorithm, Extracta mathematicae 13 1 (1998) 21–26.
  127. R. Barrio, A Elipe and M Vallejo. Compression Ephemerides in Attitude Dynamics (AAS 98-207), Advances in the Astronautical Sciences 99 (1998) 1519–1532.
  128. R. Barrio and J. Berges. Perturbation simulations of rounding errors in the evaluation of Chebyshev series, Journal of Universal Computer Science 4 6 (1998) 561–573.
  129. R. Barrio and J. Sabadell. A parallel algorithm to evaluate chebyshev series on a message passing environment, SIAM Journal on Scientific Computing 20 3 (1998) 964–969.
  130. R. Barrio and A. Elipe. Integration of orbital motions with Chebyshev Polynomials, In International Astronomical Union Colloquium, 1997.
  131. R. Barrio and J. Palacian. Semianalytical methods for high eccentric orbits- Zonal harmonics and air drag terms, Spaceflight mechanics 1997 (1997) 331–339.
  132. R. Barrio and J. Palacian. Lie transforms for ordinary differential equations: taking advantage of the Hamiltonian form of terms of the perturbation, International journal for numerical methods in engineering 40 12 (1997) 2289–2300.