Parallel Evaluation of Chebyshev Series. - Roberto Barrio; Javier Sabadell (PP, 1997)

Perturbation Simulations of Rounding Errors in the Evaluation of Chebyshev Series. - Roberto Barrio; Jean-Claude Berges (J. Univers. Comput. Sci., 1998)

A Parallel Algorithm to Evaluate Chebyshev Series on a Message Passing Environment. - Roberto Barrio; Javier Sabadell (SIAM J. Sci. Comput., 1998)

Chebyshev collocation methods for fast orbit determination. - Roberto Barrio; Manuel Palacios; Antonio Elipe (Appl. Math. Comput., 1999)

Construction of Seminumerical Schemes: Application to the Artificial Satellite Problem. - Roberto Barrio (NAA, 2000)

Stability Analysis of Parallel Evaluation of Finite Series of Orthogonal Polynominals. - Roberto Barrio; Plamen Y. Yalamov (NAA, 2000)

Parallel Algorithms to Evaluate Orthogonal Polynomial Series. - Roberto Barrio (SIAM J. Sci. Comput., 2000)

A Unified Rounding Error Bound for Polynomial Evaluation. - Roberto Barrio (Adv. Comput. Math., 2003)

Compression of almost-periodic data. - Roberto Barrio (Appl. Math. Comput., 2003)

Algorithms for the integration and derivation of Chebyshev series. - Roberto Barrio (Appl. Math. Comput., 2004)

High-order recurrences satisfied by classical orthogonal polynomials. - Roberto Barrio; Sergio Serrano (Appl. Math. Lett., 2004)

Performance of the Taylor series method for ODEs/DAEs. - Roberto Barrio (Appl. Math. Comput., 2005)

Evaluation of the derivative of a polynomial in Bernstein form. - Roberto Barrio; Juan Manuel Peña 001 (Appl. Math. Comput., 2005)

Modifications of the method of variation of parameters. - Roberto Barrio; Sergio Serrano (Comput. Math. Appl., 2006)

Painting Chaos: a Gallery of Sensitivity Plots of Classical Problems. - Roberto Barrio (Int. J. Bifurc. Chaos, 2006)

Sensitivity Analysis of ODES/DAES Using the Taylor Series Method. - Roberto Barrio (SIAM J. Sci. Comput., 2006)

Performance of perturbation methods on orbit prediction. - Roberto Barrio; Sergio Serrano (Math. Comput. Model., 2008)

Bifurcations and Chaos in Hamiltonian Systems. - Roberto Barrio; Fernando Blesa; Sergio Serrano (Int. J. Bifurc. Chaos, 2010)

Three term recurrence for the evaluation of multivariate orthogonal polynomials. - Roberto Barrio; Juan Manuel Peña 001; Tomas Sauer (J. Approx. Theory, 2010)

Breaking the limits: The Taylor series method. - Roberto Barrio; Marcos Rodríguez; Alberto Abad; Fernando Blesa (Appl. Math. Comput., 2011)

Accurate evaluation of a polynomial in Chebyshev form. - Hao Jiang 001; Roberto Barrio; Housen Li; Xiangke Liao; Lizhi Cheng; Fang Su (Appl. Math. Comput., 2011)

Qualitative and numerical analysis of the Rössler model: Bifurcations of equilibria. - Roberto Barrio; Fernando Blesa; Angeles Dena; Sergio Serrano (Comput. Math. Appl., 2011)

Uncertainty propagation or box propagation. - Roberto Barrio; Marcos Rodríguez; Alberto Abad; Sergio Serrano (Math. Comput. Model., 2011)

Incremental manifold learning by spectral embedding methods. - Housen Li; Hao Jiang 001; Roberto Barrio; Xiangke Liao; Lizhi Cheng; Fang Su (Pattern Recognit. Lett., 2011)

High-precision computation: Mathematical physics and dynamics. - David H. Bailey; Roberto Barrio; Jonathan M. Borwein (Appl. Math. Comput., 2012)

Accurate computing elementary symmetric functions. - Hao Jiang 001; Stef Graillat; Roberto Barrio (ACM Commun. Comput. Algebra, 2012)

Computer-assisted proof of skeletons of periodic orbits. - Roberto Barrio; Marcos Rodríguez; Fernando Blesa (Comput. Phys. Commun., 2012)

Behavior Patterns in multiparametric Dynamical Systems: Lorenz Model. - Roberto Barrio; Fernando Blesa; Sergio Serrano (Int. J. Bifurc. Chaos, 2012)

Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. - Roberto Barrio; Andrey Shilnikov; Leonid Pavlovich Shilnikov (Int. J. Bifurc. Chaos, 2012)

To Escape or not to Escape, that is the Question - perturbing the HéNon-Heiles Hamiltonian. - Fernando Blesa; Jesús M. Seoane; Roberto Barrio; Miguel A. F. Sanjuán (Int. J. Bifurc. Chaos, 2012)

Algorithm 924: TIDES, a Taylor Series Integrator for Differential EquationS. - Alberto Abad; Roberto Barrio; Fernando Blesa; Marcos Rodríguez (ACM Trans. Math. Softw., 2012)

Accurate and Fast Evaluation of Elementary Symmetric Functions. - Hao Jiang 001; Stef Graillat; Roberto Barrio (IEEE Symposium on Computer Arithmetic, 2013)

Accurate, Validated and Fast Evaluation of Bézier Tensor Product Surfaces. - Hao Jiang 001; Housen Li; Lizhi Cheng; Roberto Barrio; Canbin Hu; Xiangke Liao (Reliab. Comput., 2013)

A General Condition Number for Polynomials. - Roberto Barrio; Hao Jiang 001; Sergio Serrano (SIAM J. Numer. Anal., 2013)

Systematic Computer Assisted Proofs of periodic orbits of Hamiltonian systems. - Roberto Barrio; Marcos Rodríguez (Commun. Nonlinear Sci. Numer. Simul., 2014)

Symbolic Quest into Homoclinic Chaos. - Tingli Xing; Roberto Barrio; Andrey Shilnikov (Int. J. Bifurc. Chaos, 2014)

Automatic implementation of the numerical Taylor series method: A Mathematica and Sage approach. - Alberto Abad; Roberto Barrio; Miguel Ángel Marco-Buzunáriz; Marcos Rodríguez (Appl. Math. Comput., 2015)

A database of rigorous and high-precision periodic orbits of the Lorenz model. - Roberto Barrio; Angeles Dena; Warwick Tucker (Comput. Phys. Commun., 2015)

OpenCL parallel integration of ordinary differential equations: Applications in computational dynamics. - Marcos Rodríguez; Fernando Blesa; Roberto Barrio (Comput. Phys. Commun., 2015)

Accurate, validated and fast evaluation of elementary symmetric functions and its application. - Hao Jiang 001; Stef Graillat; Roberto Barrio; Canqun Yang (Appl. Math. Comput., 2016)

Local Linear Convergence of a Primal-Dual Algorithm for the Augmented Convex Models. - Tao Sun 005; Roberto Barrio; Hao Jiang 001; Lizhi Cheng (J. Sci. Comput., 2016)

Coexistence and Dynamical Connections between Hyperchaos and Chaos in the 4D Rössler System: A Computer-Assisted Proof. - Daniel Wilczak; Sergio Serrano; Roberto Barrio (SIAM J. Appl. Dyn. Syst., 2016)

Accurate quotient-difference algorithm: Error analysis, improvements and applications. - Peibing Du; Roberto Barrio; Hao Jiang 001; Lizhi Cheng (Appl. Math. Comput., 2017)

Systematic Computer-Assisted Proof of Branches of Stable Elliptic Periodic Orbits and Surrounding Invariant Tori. - Daniel Wilczak; Roberto Barrio (SIAM J. Appl. Dyn. Syst., 2017)

ORTHOPOLY: A library for accurate evaluation of series of classical orthogonal polynomials and their derivatives. - Roberto Barrio; Peibing Du; Hao Jiang 001; Sergio Serrano (Comput. Phys. Commun., 2018)

Precompact convergence of the nonconvex Primal-Dual Hybrid Gradient algorithm. - Tao Sun 005; Roberto Barrio; Lizhi Cheng; Hao Jiang 001 (J. Comput. Appl. Math., 2018)

Bregman Proximal Gradient Algorithm With Extrapolation for a Class of Nonconvex Nonsmooth Minimization Problems. - Xiaoya Zhang; Roberto Barrio; María Angeles Martínez Carballo; Hao Jiang 001; Lizhi Cheng (IEEE Access, 2019)

Convergence rates of accelerated proximal gradient algorithms under independent noise. - Tao Sun 005; Roberto Barrio; Hao Jiang 001; Lizhi Cheng (Numer. Algorithms, 2019)

Inertial Nonconvex Alternating Minimizations for the Image Deblurring. - Tao Sun 005; Roberto Barrio; Marcos Rodríguez; Hao Jiang 001 (IEEE Trans. Image Process., 2019)

Excitable dynamics in neural and cardiac systems. - Roberto Barrio; Stephen Coombes; Mathieu Desroches; Flavio H. Fenton; Stefan Luther; Esther Pueyo (Commun. Nonlinear Sci. Numer. Simul., 2020)

Spike-adding structure in fold/hom bursters. - Roberto Barrio; Santiago Ibáñez 002; Lucía Pérez; Sergio Serrano (Commun. Nonlinear Sci. Numer. Simul., 2020)

Numerical detection of patterns in CPGs: Gait patterns in insect movement. - Roberto Barrio; Álvaro Lozano-Rojo; Marcos Rodríguez; Sergio Serrano (Commun. Nonlinear Sci. Numer. Simul., 2020)

Experimentally Accessible Orbits Near a Bykov Cycle. - Roberto Barrio; Maria Carvalho; Luísa Castro; Alexandre A. P. Rodrigues (Int. J. Bifurc. Chaos, 2020)

A High-Precision DQDS Algorithm. - Chuanying Li; Xiong Xiao; Peibing Du; Hao Jiang 001; Roberto Barrio; Zhe Quan; Kenli Li 001 (HPCC/DSS/SmartCity/DependSys, 2021)

Quantization improvements for LU Decomposition to Solve Linear Equations. - Lin Chen 028; Kang He; Hao Jiang 001; Roberto Barrio; Jie Liu 002; Tiejun Li (ISPA/BDCloud/SocialCom/SustainCom, 2021)

A Class of Fast and Accurate Multi-layer Block Summation and Dot Product Algorithms. - Kang He; Roberto Barrio; Lin Chen 028; Hao Jiang 001; Jie Liu 002; Tongxiang Gu; Jin Qi (NPC, 2021)

Routes to tripod gait movement in hexapods. - Roberto Barrio; Álvaro Lozano-Rojo; María Angeles Martínez Carballo; Marcos Rodríguez; Sergio Serrano (Neurocomputing, 2021)

PACF: A precision-adjustable computational framework for solving singular values. - Chuanying Li; Roberto Barrio; Xiong Xiao; Peibing Du; Hao Jiang 001; Zhe Quan; Kenli Li 001 (Appl. Math. Comput., 2023)

A mechanism for growth of topological entropy and global changes of the shape of chaotic attractors. - Daniel Wilczak; Sergio Serrano; Roberto Barrio (CoRR, 2025)