José Luis Morales

Universidad Nacional Autónoma de México

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Jorge Nocedal

Northwestern University

F. Alhama

Universidad Politécnica de Cartagena

Juana Moreno

Louisiana State University

Iván Alhama

Universidad Politécnica de Cartagena

Ciyou Zhu

Northwestern University

Richard Byrd

University of Colorado Boulder

Patrizia Calaminici

Instituto Politécnico Nacional

Andreas M. Köster

Instituto Politécnico Nacional

John C. Nash

University of Ottawa

Jesús N. Pedroza-Montero

Instituto Politécnico Nacional

Cooperative Institutions

Center for Research and Advanced Studies of the National Polytechnic Institute

Instituto Politécnico Nacional

Universidad Politécnica de Cartagena

Northwestern University

Centre National de la Recherche Scientifique

University of Cartagena

Universidad Nacional Autónoma de México

Biblioteca Nacional de España

Equilibrium Research

Instituto de Estudios Avanzados

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Robust and efficient density fitting

The Journal of Chemical Physics (2009)

Víctor Domínguez-Soria Gerald Geudtner José Luis Morales Patrizia Calaminici Andreas M. Köster

In this paper we propose an iterative method for solving the inhomogeneous systems of linear equations associated with density fitting. The proposed method is based on a version of the conjugate gradient method that makes use of automatically built quasi-Newton preconditioners. The paper gives a detailed description of a parallel implementation of the new method. The computational performance of the new algorithms is analyzed by benchmark calculations on systems with up to about 35 000 auxiliary functions. Comparisons with the standard, direct approach show no significant differences in the computed solutions.

Benchmark (surveying)

10.1063/1.3216476

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Citations (28)

A systematic literature review of the Teleo-Reactive paradigm

Artificial Intelligence Review (2012)

José Luis Morales Pedro Sánchez Diego Alonso

10.1007/s10462-012-9350-2

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Citations (18)

New additional conditions for the numerical uniqueness of the Boussinesq and Timpe solutions of elasticity problems

International Journal of Computer Mathematics (2012)

José Luis Morales Juana Moreno F. Alhama

New additional simple conditions of Dirichlet type are proposed for the numerical uniqueness of the solution of elastostatic axisymmetric problems formulated in terms of Boussinesq and Timpe potential functions, as particular cases of the Papkovich–Neuber representation. Applications to hollow cylinder, subjected to general axisymmetric load and displacement boundary conditions, are shown and numerically solved by the network method.

Elasticity

10.1080/00207160.2012.667088

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Citations (16)

Numerical solution of 2D elastostatic problems formulated by potential functions

Applied Mathematical Modelling (2013)

José Luis Morales Juana Moreno F. Alhama

Vector-valued function

Scalar potential

Potential theory

10.1016/j.apm.2013.01.030

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Citations (5)

Numerical Solutions of 2-D Linear Elastostatic Problems by Network Method

Computer Modeling in Engineering & Sciences (2011)

José Luis Morales Juana Moreno F. Alhama

10.3970/cmes.2011.076.001

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Citations (11)

On the solution of complementarity problems arising in American options pricing

Optimization methods & software (2010)

Liming Feng Vadim Linetsky José Luis Morales Jorge Nocedal

Abstract In the Black–Scholes–Merton model, as well as in more general stochastic models in finance, the price of an American option solves a parabolic variational inequality. When the variational inequality is discretized, one obtains a linear complementarity problem (LCP) that must be solved at each time step. This paper presents an algorithm for the solution of these types of LCPs that is significantly faster than the methods currently used in practice. The new algorithm is a two-phase method that combines the active-set identification properties of the projected successive over relaxation (SOR) iteration with the second-order acceleration of a (recursive) reduced-space phase. We show how to design the algorithm so that it exploits the structure of the LCPs arising in these financial applications and present numerical results that show the effectiveness of our approach. Keywords: American options pricinglinear complementarityprojected SOR method Acknowledgements The authors are grateful to Jong-Shi Pang for his comments and advice during the preparation of this manuscript. L. Feng was supported by National Science Foundation grant CMMI-0927367. V. Linetsky was supported by National Science Foundation grant DMS-0802720. J.L. Morales was supported by Asociación Mexicana de Cultura AC and CONACyT-NSF grant J110.388/2006. J. Nocedal was supported by National Science Foundation grant DMS-0810213 and Department of Energy grant DE-FG02-87ER25047-A004.

Linear complementarity problem

Complementarity (molecular biology)

10.1080/10556788.2010.514341

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Citations (20)

Application of the network method to simulate elastostatic problems defined by potential functions. Applications to axisymmetrical hollow bodies

International Journal of Computer Mathematics (2012)

José Luis Morales Juana Moreno F. Alhama

The direct application of the network method for the numerical solution of 2D linear elastostatic problems formulated by potential functions has demonstrated to be a powerful tool that provides accurate solutions with small computational times. The method is used for solving axisymmetrical problems formulated by two (Boussinesq and Timpe) or three (Papkovich–Neuber) displacement potentials. The network method makes most of the potent computational algorithms implemented in electrical simulation codes and allows an easy implementation of the complex boundary conditions inherent to this potential formulation in comparison with other classical numerical methods. The application to a hollow cylinder subjected to general load boundary conditions is presented by comparing the elastic solution with those provided by other formulations.

10.1080/00207160.2012.663910

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Citations (17)

An algorithm for the fast solution of symmetric linear complementarity problems

Numerische Mathematik (2008)

José Luis Morales Jorge Nocedal Mikhail Smelyanskiy

Linear complementarity problem

Complementarity (molecular biology)

Krylov subspace

Interior point method

Projection method

10.1007/s00211-008-0183-5

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Citations (38)

An example of gaussian molecular orbital ab-initio calculations including configuration interaction. The h2 molecule

Revista Mexicana de Física (1980)

José Luis Morales P.G Del Conde

Fragment molecular orbital

Hydrogen molecule

Gaussian orbital

Source

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Citations (0)

Algorithm 809: PREQN

ACM Transactions on Mathematical Software (2001)

José Luis Morales Jorge Nocedal

PREQN is a package of Fortran 77 subroutins for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems A i x = b i , i = 1…, t , where the coefficient matrices A i are symmetric and positive definite and vary slowly. Problems of this type arise, for example, in nonlinear optimization. The preconditioners are based on limited-memory quasi-Newton updating and are recommended for problems in which (i) the coefficient matrices are not explicitly known and only matrix-vector products of the form A i v can be computed; or (ii) the coefficient matrices are not sparse. PREQN is written so that a single call from a conjugate gradient routine performs the preconditioning operation and stores information needed for the generation of a new preconditioner.

Coefficient matrix

Fortran

Matrix (chemical analysis)

Sequence (biology)

Conjugate

10.1145/382043.382343

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Citations (21)