Marcos Raydan

Publications:

 Books:  
 
  
Métodos Iterativos tipo Krylov para Sistemas Lineales,  Ed: Centro de Estudios Avanzados, Instituto de
   Investigaciones Científicas (IVIC), Caracas, Venezuela, (with  B. Molina), (2004). ISBN: 980-261-078-X.

   Alternating Projection Methods, SIAM, (with  René Escalante), (2011). ISBN 978-1-611971-93-4.

 Papers:  

    Inexact Newton's method with inner implicit preconditioning for algebraic Riccati equations, Computational and Applied Mathematics, to appear, (2016) (con Jean-Paul Chehab).

   Geometrical inverse preconditioning for symmetric positive definiite matrices, Mathematics, Vol. 4, 46, doi:10.3390/math4030046, (2016) (with Jean-Paul Chehab).

  Inverse-free recursive multiresolution algorithms for a data approximation problem, Computers and Mathematics with Applications, Vol. 72, 1177-1187, (2016)  (with M. A. Fortes and A. M. Sajo-Castelli).

  An acceleration scheme for Dykstra's algorithmComputational Optimization and Applications,  Vol. 63, 29-44, (2016),  (with  Williams López).

  An inner-outer nonlinear programming approach for constrained quadratic matrix model updating, Mechanical Systems and Signal Processing,  Vol. 66-67, 78-88, (2016)  (with M. Andretta and E. Birgin).

  Separable cubic modeling and a trust-region strategy for unconstrained minimization with impact in global optimization, Journal of Global Optimization,  Vol. 63, Issue 2, 319-342, (2015) (with  J. M. Martínez).

Preconditioned conjugate gradient method for finding minimal energy surfaces on Powell - Sabin triangulations, Journal of Computational and Applied Mathematics,  Vol. 268, 34-55, (2014) (with A. M. Sajo-Castelli y M. A. Fortes).

 Spectral Projected Gradient methods: Review and Perspectives, Journal of Statistical Software, Vol. 60, Issue 3,  (2014)   (with Ernesto Birgin and J. M. Martínez).

Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems, Bulletin of Computational Applied Mathematics, Vol. 1, 25-47,  (2013)  (with Oskar Cahueñas and  Luis M. Hernández-Ramos)

 On the geometrical structure of symmetric matrices, Linear Algebra and its Applications, Vol. 438, 1201-1214,  (2013)  
 (with Roberto Andreani and Pablo Tarazaga).

 A hybrid-optimization method for large-scale non-negative  full regularization in image restoration, Inverse Problems in  
Science & Engineering,  Vol. 21, 741-766 (2013), (with Johana Guerrero and Marielba Rojas).

Newton's method and  secant methods: A longstanding relationship from vectors to matrices, Portugaliae Mathematica, Vol. 68, 431-475 (2011) (with Marlliny Monsalve).

Unconstrained optimization techniques for the  acceleration of alternatingprojection methods
Numerical Functional Analysis and Optimization, Vol. 32, 1041-1066 (2011) (with Luis M. Hernández-Ramos and R. Escalante).

An implicit preconditioning strategy for large-scale  generalized Sylvester equationsApplied Mathematics and Computation, Vol. 217, 8793-8803 (2011) (with Jean-Paul Chehab).

Convex constrained optimization for large-scale generalized Sylvester equations, Computational Optimization and Applications, Vol. 48, 233-253 (2011) (with A. Bouhamidi and K. Jbilou). 

A secant method for nonlinear matrix problems, Special Volume in Numerical Linear Algebra in Signals,
 Systems and Control, Springer, Series: Lecture Notes in Electrical Engineering, Vol.  80, Van Dooren, P.;  Bhattacharyya, S. P.; Chan, R. H.; Olshevsky, V.; Routray, A. (Eds.), Chapter 19 (2011)  (with  Marlliny  Monsalve). 

Computing a nearest correlation matrix with factor structure, SIAM J. Matrix Analysis and Applications, Vol. 31, 2603-2622 (2010) (with Rüdiger Borsdorf and Nicholas J. Higham).

Residual methods for the large-scale matrix p-th root and some related problems, Applied Mathematics and Computation, Vol. 217, 650-660 (2010) (with Braulio De Abreu).

Residual algorithm for large-scale generalized eigenvalue problems, Computational Optimization and Applications, Vol. 46, 217-227 (2010) (with Lenys Bello and William La Cruz).

A new inversion-free method for a rational matrix equation, Linear Algebra and its Applications, Vol. 433, 64-71 (2010) (with Marlliny Monsalve).

Implicitly preconditioned and globalized residual method for solving steady fluid flows, Electronic Transactions on Numerical Analysis (ETNA), Vol. 34, 136-151, (2009) (with Jean Paul Chehab).

A symmetry preserving alternating projection method for matrix model updating, Mechanical Systems and Signal Processing, Vol. 23, 1784-1791, (2009) (with Joali Moreno and Biswa Datta).

Dykstra's algorithm and robust stopping criteria,   in: Encyclopedia of Optimization, Second Ed., Editors:  C. A. Floudas and P. M. Pardalos, Part 4, pp. 828-833, (2009) (with Ernesto Birgin).  ISBN:978-0-387-74759-0.

Spectral Projected Gradient Methods, in: Encyclopedia of Optimization, Second Ed., Editors:  C. A. Floudas and P. M. Pardalos, Part 19, pp. 3652-3659, (2009) (with E. Birgin and J. M. Martínez).
 ISBN: 978-0-387-74759-0.

Geometrical properties of the Frobenius condition number for positive definite matrices, Lineal Algebra and its Applications, Vol. 429, pp. 2089-2097, (2008) (with Jean Paul Chehab).

Specialized and hybrid Newton schemes for the matrix p-th root, Applied Mathematical Sciences, Vol. 2, No. 49, pp. 2401-2424, (2008) (with B. De Abreu and M. Monsalve).

Residual iterative schemes for large-scale nonsymmetric positive definite linear systems, Computational and Applied Mathematics, Vol. 27, pp. 151-173, (2008) (with William La Cruz).

A derivative--free tolerant line search technique for unconstrained optimization, Journal of Computational and Applied Mathematics, Vol. 219, pp. 383-397, (2008) (with M. A. Diniz-Ehrhardt and J. M. Martínez).

On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm, Numerical Algorithms, Vol. 47, pp. 391-407, (2008) (with J.J. Judice, S. Rosas and S. Santos).

Convex-Constrained Optimization for the Seismic Reflection Tomography Problem, Journal of Applied Geophysics, Vol. 62, pp. 158-166, (2007) (with Lenys Bello).

Spectral Projected Subgradient with a Momentum Term for the Lagrangean Dual Approach, Computers and Operations Research, Vol. 34, pp. 3174-3186, (2007) (with A. Crema and M. Loreto).

Cauchy-Schwarz and Kantorovich type Inequalities for Scalar and Matrix Moment Sequences, Advances in Computational Mathematics, Vol. 26, pp. 71-80, (2007) (with Claude Brezinski).

Spectral Residual Method without Gradient Information for Solving Large-Scale Nonlinear Systems of Equations, Mathematics of Computation, Vol. 75, pp. 1449-1466, (2006) (with W. La Cruz and J. M. Martínez). [Pdf file] [Fortran Code]

Implicit and Adaptive Inverse Preconditioned Gradient Method for Nonlinear Problems, Applied Numerical Mathematics, Vol. 55, pp. 32-47, (2005) (with Jean Paul Chehab).

Preconditioned Spectral Projected Gradient Methods on Convex Sets, Journal of Computational Mathematics, Vol. 23, pp. 225-232 (2005) (with Lenys Bello).

Robust Stopping Criteria for Dykstra's Algorithm, SIAM J. Sci. Comp., Vol. 26, pp. 1405-1414, (2005) (with Ernesto Birgin).

Spectral Gradient Methods for Linearly Constrained Optimization, Journal of Optimization Theory and Applications, Vol. 125, pp. 629-651 (2005) (with J. M. Martínez and E. Pilotta).

Low Cost Methods for Nonlinear Large-Scale Matrix Equations, in Y. Yuan, ed., Numerical Linear Algebra and Optimization, (Science Press, Beijing), pp.79-87 (2004).

Nonmonotone Spectral Methods for Large-Scale Nonlinear Systems, Optimization Methods and Software, Vol. 18, pp. 583-599 (2003) (with William La Cruz). [Fortran Code]

Gradient Method with Dynamical Retards for Large-Scale Optimization Problems, Electronic Transactions on Numerical Analysis (ETNA), Vol. 16, pp. 186-193 (2003) (with Francisco Luengo).

Inexact Spectral Projected Gradient Methods on Convex Sets, IMA Journal of Numerical Analysis, Vol. 23, pp. 539-559 (2003) (with Ernesto Birgin and J. M. Martínez).

 Selective Alternating Projections to Find the Nearest SDD+ Matrix, Applied Mathematics and Computation, Vol. 145, pp. 205-220 (2003) (with M. Monsalve, J. Moreno and R. Escalante).

•  Smooth and Adaptive Gradient Method with Retards, Mathematical and Computer Modelling, Vol. 36, pp. 1161-1168 (2002) (with J. L. Lamotte and B. Molina).

Preconditioned Spectral Gradient Method, Numerical Algorithms, Vol. 30, pp. 241-258 (2002) (with F. Luengo, W. Glunt and T.L. Hayden).

 Primal and Polar Approach for Computing the Symmetric Diagonally Dominant Projection, Numerical Linear Algebra with Applications, Vol. 9, pp. 333-345 (2002), (with Pablo Tarazaga).

Spectral Variants of Krylov Subspace Methods, Numerical Algorithms, Vol. 29, pp. 197-208 (2002), (with Brigida Molina).

Relaxed Steepest Descent and Cauchy-Barzilai-Borwein Method, Computational Optimization and Applications, Vol. 21, pp. 155-167 (2002), (with Benar Svaiter).

Algorithm 813: SPG - Software for Convex-Constrained Optimization, ACM Transactions on Mathematical Software, Vol. 27, pp. 340-349 (2001), (with E. G. Birgin and J. M. Martínez).

Perron-Frobenius Theorem for Matrices with Some Negative Entries, Linear Algebra and its Applications, Vol. 328, pp. 57-68 (2001), (with Pablo Tarazaga and Ana Hurman).

•  Low Cost Optimization Techniques for Solving the Nonlinear Seismic Reflection Tomography Problem, Optimization and Engineering, Vol. 1, pp. 155-169 (2000), (with Z. Castillo and Debora Cores).

•  An Assesment of the Preconditioned Gradient Method with Retards for Parallel Computers, Computational and Applied Mathematics, Vol. 19, pp. 323-337, (2000), (with B. Molina and S. Petiton).

•  Theoretical Analysis of Exponential Transversal Method of Lines for the Diffusion Equation, Numerical Methods for Partial Differential Equations, Vol. 12, pp. 30-42, (2000), (with Abraham Salazar and Antonio Campo).

•  Nonmonotone Spectral Projected Gradient Methods on Convex Sets, SIAM Journal on Optimization, Vol.10, pp. 1196-1211, (2000), (with E. G. Brigin and J.M. Martínez).

•  Computing the Symmetric Diagonally Dominant Projection via Duality, Proceedings of the XV Interuniversity Mathematical Research Seminar (XV SIDIM), University of Puerto Rico, Mayaguez Campus, Puerto Rico, pp. 59-76, (2000), (with Pablo Tarazaga).

•  Gradient Method with Retards and Generalizations, SIAM Journal on Numerical Analysis, Vol. 36, pp. 275-289, (1999), (with Ana Friedlander, J. M. Martínez and B. Molina).

•   Computing the Nearest Diagonally Dominant Matrix, Numerical Linear Algebra with Applications, Vol. 5, pp. 461-474, (1998), (with Maria Mendoza and Pablo Tarazaga).

• Dykstra's Algorithm for Constrained Least-Squares Rectangular Matrix Problems, Computers and Mathematics with Applications, Vol. 35, pp. 73-79, (1998), (with Rene Escalante).

•  An Adaptive Algorithm for Bound Constrained Quadratic Minimization, Investigacion Operativa, Vol. 7, pp. 67-102, (1997), (with R. H. Bielschowsky, Ana Friedlander, F. M. Gomes and J. M. Martínez).

•  Preconditioned Gradient Method with Retards for Parallel Computers, Proceedings of the III National Meeting on Parallel and Distributed Computing, Merida, Venezuela, pp. 91-98, (1997), (with B. Molina and S. Petiton).

The Barzilai and Borwein Gradient Method for the Large-Scale Unconstrained Minimization Problem, SIAM Journal on Optimization, Vol. 7, pp. 26-33, (1997).

•  Theoretical Analysis of Exponential Transversal Method of Lines for the Diffusion Equation, Proceedings of the 31st National Heat Transfer Conference, Houston, Texas, USA, ASME Publications, Vol. 331, pp. 95-102, (1996), (with Abraham Salazar and Antonio Campo).

• Dykstra's Algorithm for a Constrained Least-Squares Matrix Problem, Numerical Linear Algebra with Applications, Vol. 3, pp. 459-471, (1996), (with Rene Escalante).

The Preconditioned Barzilai-Borwein Method for the Numerical Solution of Partial Differential Equations, Numerical Algorithms, Vol. 13, pp. 45-60, (1996), (with B. Molina).

•  A New Method for Large-Scale Box Constrained Convex Quadratic Minimization Problems, Optimization Methods and Software, Vol. 5, pp. 57-74, (1995), (with Ana Friedlander and J. M. Martínez).

Preconditioners for Distance Matrix Algorithms, Journal of Computational Chemistry, Vol. 15, pp. 227-232, (1994), (with W. Glunt and T.L. Hayden).

Exact Order of Convergence of the Secant Method, Journal of Optimization Theory and Applications, Vol. 78, pp. 541-551, (1993).

Molecular Conformations from Distance Matrices, Journal of Computational Chemistry, Vol. 14, pp. 114-120, (1993), (with W. Glunt and T.L. Hayden).

On the Barzilai and Borwein Choice of Steplength for the Gradient Method, IMA Journal of Numerical Analysis, Vol. 13, pp. 321-326, (1993).

A General Algorithm in Optimal Control Problems, Acta Cientifica Venezolana, Vol. 40, pp. 174-180, (1989),  
(with José Aguilera).

Comparison of Several Codes for Solving Large Sparse Linear Systems, Acta Cientifica Venezolana, Vol. 36, pp. 100-102, (1985), (with H. Lopez, C. Maulino, V. Pereyra and A. Sanchez).



 



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