Papers by Violeta Migallón
The analysis of climate variability requires to perform operations with netCDF flles (1), Empiric... more The analysis of climate variability requires to perform operations with netCDF flles (1), Empirical Orthogonal Functions analysis (EOF), and Singular Value Decompositions (SVD) of coupled data sets. As example, PyClimate (2) is a Python package designed to accomplish these tasks sequentially. However, the huge data volume in this kind of applications requires high performance routines that can be executed in
Journal of Parallel and Distributed Computing, 2012
In this work we describe some parallel algorithms for solving nonlinear systems using CUDA (Compu... more In this work we describe some parallel algorithms for solving nonlinear systems using CUDA (Compute Unified Device Architecture) over a GPU (Graphics Processing Unit). The proposed algorithms are based on both the Fletcher-Reeves version of the nonlinear conjugate gradient method and a polynomial preconditioner type based on block two-stage methods. Several strategies of parallelization and different storage formats for sparse matrices are discussed. The reported numerical experiments analyze the behavior of these algorithms working in a fine grain parallel environment compared with a thread-based environment.
The Journal of Supercomputing, 2011
Parallel nonlinear preconditioners, for solving mildly nonlinear systems, are proposed. These alg... more Parallel nonlinear preconditioners, for solving mildly nonlinear systems, are proposed. These algorithms are based on both the Fletcher-Reeves version of the nonlinear conjugate gradient method and a polynomial preconditioner type based on block two-stage methods. The behavior of these algorithms is analyzed when incomplete LU factorizations are used in order to obtain the inner splittings of the block two-stage method. As our illustrative example we have considered a nonlinear elliptic partial differential equation, known as the Bratu problem. The reported experiments show the performance of the algorithms designed in this work on two multicore architectures.
Numerische Mathematik, 1999
Block parallel iterative methods for the solution of mildly nonlinear systems of equations of the... more Block parallel iterative methods for the solution of mildly nonlinear systems of equations of the form \(Ax=\Phi(x)\) are studied. Two-stage methods, where the solution of each block is approximated by an inner iteration, are treated. Both synchronous and asynchronous versions are analyzed, and both pointwise and blockwise convergence theorems provided. The case where there are overlapping blocks is also considered. The analysis of the asynchronous method when applied to linear systems includes cases not treated before in the literature.
Computing Systems in Engineering, 1995
Chaotic synchronous and asynchronous schemes based on two-stage methods to solve nonsingular line... more Chaotic synchronous and asynchronous schemes based on two-stage methods to solve nonsingular linear systems are presented. The convergence of these schemes is studied either when the chaotic parameters become sufficiently large or when the matrix in question is monotone• The results are illustrated by computational experiments on a shared memory multiprocessor vector computer•
Bit Numerical Mathematics, 2003
Parallel Newton two-stage iterative methods to solve nonlinear systems are studied. These algorit... more Parallel Newton two-stage iterative methods to solve nonlinear systems are studied. These algorithms are based on both the multisplitting technique and the two-stage iterative methods. Convergence properties of these methods are studied when the Jacobian matrix is either monotone or an H-matrix. Furthermore, in order to illustrate the performance of the algorithms studied, computational results about these methods on a distributed memory multiprocessor are discussed.
The Journal of Supercomputing
Parallel nonlinear preconditioners, for solving mildly nonlinear systems, are proposed. These alg... more Parallel nonlinear preconditioners, for solving mildly nonlinear systems, are proposed. These algorithms are based on both the Fletcher–Reeves version of the nonlinear conjugate gradient method and a polynomial preconditioner type based on block two-stage methods. The behavior of these algorithms is analyzed when incomplete LU factorizations are used in order to obtain the inner splittings of the block two-stage method. As our illustrative example we have considered a nonlinear elliptic partial differential equation, known as the Bratu problem. The reported experiments show the performance of the algorithms designed in this work on two multicore architectures.
Journal of Parallel and Distributed Computing
In this work we describe some parallel algorithms for solving nonlinear systems using CUDA (Compu... more In this work we describe some parallel algorithms for solving nonlinear systems using CUDA (Compute Unified Device Architecture) over a GPU (Graphics Processing Unit). The proposed algorithms are based on both the Fletcher-Reeves version of the nonlinear conjugate gradient method and a polynomial preconditioner type based on block two-stage methods. Several strategies of parallelization and different storage formats for sparse matrices are discussed. The reported numerical experiments analyze the behavior of these algorithms working in a fine grain parallel environment compared with a thread-based environment.
Linear Algebra and Its Applications, 1996
Relaxed nonstationary multisplitting methods are studied for the parallel solution of nonsingular... more Relaxed nonstationary multisplitting methods are studied for the parallel solution of nonsingular linear systems. Convergence results of the synchronous and asynchronous versions for systems with H-matrices are presented. Computational results of these methods on a shared memory multiprocessor vector computer are reported. These results show that nonstationary methods (synchronous and asynchronous) are better than the standard ones, especially when the matrix of the linear system has a relatively small bandwidth. Moreover, asynchronous versions always behave better than the synchronous ones. *
Resumen: Este trabajo se centra en una de las asignaturas de primer curso de las titulaciones de ... more Resumen: Este trabajo se centra en una de las asignaturas de primer curso de las titulaciones de Informática: Matemática Discreta, y el objetivo principal es explicar y analizar las actividades, que desde el curso 2003-2004, se están realizando en dicha asignatura para su adaptación a los créditos ECTS. Estas actividades se realizan dentro del marco del proyecto piloto de implementación ECTS de las asignaturas de primero de las titulaciones de Informática.
The ACTS collection project comprises a set of state-of-the-art software tools to speed up the de... more The ACTS collection project comprises a set of state-of-the-art software tools to speed up the development of High-Performance Computing Applications in science and engineering. We look at the development of High Level user interfaces using scripting languages like Python, to facilitate the access to ACTS technology to a wide community of computational scientists. PyACTS is our main project here, but we also visit other efforts within the community of developers of ACTS tools.
Numerical Linear Algebra With Applications, 1996
The use of block two-stage methods for the iterative solution of consistent singular linear syste... more The use of block two-stage methods for the iterative solution of consistent singular linear systems is studied. In particular, hypotheses are provided for the convergence of non-stationary methods, i.e., when the number of inner iterations may vary from block to block and from one outer iterations to another.
Parallel algorithms for solving almost linear systems are studied. A non-stationary parallel algo... more Parallel algorithms for solving almost linear systems are studied. A non-stationary parallel algorithm based on the multi-splitting technique and its extension to an asynchronous model are considered. Convergence properties of these methods are studied for M-matrices and H-matrices. We implemented these algorithms on two distributed memory multiprocessors, where we studied their performance in relation to overlapping of the splittings at each iteration.
Numerical Linear Algebra With Applications, 1999
Non-stationary parallel multisplitting iterative methods are introduced for the solution of almos... more Non-stationary parallel multisplitting iterative methods are introduced for the solution of almost linear systems. A non-stationary parallel algorithm based on the AOR-type methods and its extension to asynchronous models are considered. Convergence properties of the synchronous and asynchronous versions of these methods are studied for M-matrices and H -matrices. Furthermore, computational results about these methods on a distributed memory multiprocessor, which illustrate the performance of the algorithms studied, are discussed.
Software reusability has proven to be an effective practice to speed-up the development of comple... more Software reusability has proven to be an effective practice to speed-up the development of complex high-performance scientific and engineering applications. We promote the reuse of high quality software and general purpose libraries through the Advance CompuTational Software (ACTS) Collection. ACTS tools have continued to provide solutions to many of today’s computational problems. In addition, ACTS tools have been successfully ported to a variety of computer platforms; therefore tremendously facilitating the porting of applications that rely on ACTS functionalities. In this contribution we discuss a high-level user interface that provides a faster code prototype and user familiarization with ACTS tools. The high-level user interfaces have been built using Python. Here we focus on Python based interfaces to ScaLAPACK, the PyScaLAPACK component of PyACTS. We briefly introduce their use, functionalities, and benefits. We illustrate a few simple example of their use, as well as exemplar utilization inside large scientific applications. We also comment on existing Python interfaces to other ACTS tools. We present some comparative performance results of PyACTS based versus direct LAPACK and ScaLAPACK code implementations.
Applied Mathematics Letters, 1997
Two-stage iterative methods for the solution of linear systems are studied. Convergence of both s... more Two-stage iterative methods for the solution of linear systems are studied. Convergence of both stationary and nonstationary cases is analyzed when the coefficient matrix is Hermitian positive definite.
Many computational applications rely heavily in high performing numerical linear algebra oper- at... more Many computational applications rely heavily in high performing numerical linear algebra oper- ations. A good number of these applications are data and computation intensive that need to run in high performance computing environments. Researchers and engineers behind these applications have to spend a considerable amount of time efficiently developing and running codes in these en- vironments. Developers would rather devote
Linear Algebra and Its Applications, 1996
Parallel chaotic schemes based on the extrapolated Jacobi method and a second degree stationary m... more Parallel chaotic schemes based on the extrapolated Jacobi method and a second degree stationary method are studied. Sufficient conditions for the convergence of the above methods for the synchronous and asynchronous models are given. These sufficient conditions are related to properties of the block Jacobi matrix. The schemes are illustrated by computational results on a shared memory multiprocessor vector computer.
Applied Mathematics Letters, 1999
Two-stage iterative methods for the solution of linear systems are analyzed when the coefficient ... more Two-stage iterative methods for the solution of linear systems are analyzed when the coefficient matrix is Hermitian positive definite. Comparison theorems, based on the number of inner iterations performed, are given. (~)
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Papers by Violeta Migallón