Papers by Bernard Philippe
Linear Algebra, Numerical
Encyclopedia of Parallel Computing, 2011
A Slepian framework for the inverse problem of equivalent gravitational potential generated by discrete point masses
Inverse Problems in Science and Engineering, 2014
Localized spectral analysis for an inverse problem in geodesy
CARI, 2008
ABSTRACT. A distribution of ponctual masses (caracterized by its intensities and positions) is de... more ABSTRACT. A distribution of ponctual masses (caracterized by its intensities and positions) is determinated, in such a way that the associated equivalent potential best approximates a given potential field. For this purpose, a geodetic inverse problem is solved. On the whole unit sphere a potential function is usually expressed in spherical harmonics, basis functions with global support. The identification of the two potentials is done by solving a least-squares problem. When a limited area is studied, the estimation of the point-mass ...
Claude Lobry : "Coopérer en évitant tout paternalisme" ; Bernard Philippe : "Notre... more Claude Lobry : "Coopérer en évitant tout paternalisme" ; Bernard Philippe : "Notre crédibilité sur le continent africain est en jeu" ; Mohamed Jaoua et Dominique Sotteau : "Le partenariat doit se substituer à l'aide au développement"
The Davidson Method
SIAM Journal on Scientific Computing, 1994
ABSTRACT Authors’ summary: This paper deals with the method of E. R. Davidson [J. Comput. Phys. 1... more ABSTRACT Authors’ summary: This paper deals with the method of E. R. Davidson [J. Comput. Phys. 17, 87-94 (1975; Zbl 0293.65022)] that computes a few of the extreme eigenvalues of a symmetric matrix and corresponding eigenvectors. A general convergence result for methods based on projection techniques is given and can be applied to the Lanczos method as well. The efficiency of the preconditioner involved in the method is discussed. Finally, by means of numerical experiments, the Lanczos and Davidson methods are compared and a procedure for a dynamic restarting process is described.
Parallel algorithms on the cedar system
Lecture Notes in Computer Science, 1986
1. INTRODUCTION One of the key factors in the success of a supercomputer is the use of parallelis... more 1. INTRODUCTION One of the key factors in the success of a supercomputer is the use of parallelism in forms which can be effectively exploited in the design of algorithms for a large class of problems. The introduction of pipelined architectures, such as the CRAY and CYBER ...
Lecture Notes in Computer Science, 2003
Numerical Methods in Markov Chain Modelling
Operations Research, 1996
This paper describes and compares several methods for computing stationary probabilitydistributio... more This paper describes and compares several methods for computing stationary probabilitydistributions of Markov chains. The main linear algebra problem consists ofcomputing an eigenvector of a sparse, non-symmetric, matrix associated with a knowneigenvalue. It can also be cast as a problem of solving a homogeneous, singular linearsystem. We present several methods based on combinations of Krylov subspacetechniques, single vector power iteration/relaxation
International Journal for Numerical Methods in Engineering, 2002
SUMMARY The abundant literature ofnite-element methods applied to linear parabolic problems, gene... more SUMMARY The abundant literature ofnite-element methods applied to linear parabolic problems, generally, pro- duces numerical procedures with satisfactory properties. However, some initial-boundary value problems may cause large gradients at some points and consequently jumps in the solution that usually needs a certain period of time to become more and more smooth. This intuitive fact of the diusion process necessitates, when
Numerical reliability for mixed methods applied to flow problems in porous media
This paper is devoted to the numerical reliability and time requirements of the Mixed Finite Elem... more This paper is devoted to the numerical reliability and time requirements of the Mixed Finite Element (MFE) and Mixed-Hybrid Finite Element (MHFE) methods. The behavior of these methods is investigated under the influence of two factors: the mesh discretization and the medium heterogeneity. We show that, unlike the MFE, the MHFE suffers with the presence of badly shaped discretized elements.
PAT – a Reliable Path-Following Algorithm
Numerical Algorithms, 2002
This paper presents a new technique for the reliable computation of the s-pseudospectrum defined ... more This paper presents a new technique for the reliable computation of the s-pseudospectrum defined by ?s(A)={z?C : smin(A-zI)=s} where smin is the smallest singular value. The proposed algorithm builds an orbit of adjacent equilateral triangles to capture the level curve ?s(A)={z?C : smin(A-zI)=s} and uses a bisection procedure on specific triangle vertices to compute a numerical approximation to ?s. The
Parallel computation of pseudospectra of large sparse matrices
Parallel Computing, 2002
The parallel computation of the pseudospectrum is presented. The Parallel Path following Algorith... more The parallel computation of the pseudospectrum is presented. The Parallel Path following Algorithm using Triangles (PPAT) is based on the Path following Algorithm using Triangles (PAT). This algorithm offers total reliability and can handle singular points along the level curve without difficulty. Furthermore, PPAT offers a guarantee of termination even in the presence of round-off errors and makes use of
Parallel computation of spectral portrait of large matrices
Lecture Notes in Computer Science, 1996
... and storage. However, noticing that a2mi~(A - zI) = A,~((A - zI)H(A -- zI)) where Ami,, denot... more ... and storage. However, noticing that a2mi~(A - zI) = A,~((A - zI)H(A -- zI)) where Ami,, denotes the smallest eigenvalue, one may use an efficient sparse symmetric eigenvalue solver for computing the smallest eigenvMue. In [2 ...
Arnoldi’s procedure and angles between Krylov subspaces
When a Krylov subspace method is applied to a non-Hermitian matrix A∈ℂ n×n it produces, at step m... more When a Krylov subspace method is applied to a non-Hermitian matrix A∈ℂ n×n it produces, at step m, a matrix V m , whose columns are orthonormal and candidate for spanning an invariant subspace for A. The purpose of this note is to propose a way to evaluate the evolution of the canonical angles between span{V m } and span{AV m } and between span{V m } and span{A m v 1 } where V m =[v 1 ,v 2 ,⋯,v m ] is generated by a block-Arnoldi method.
Aquarels: A problem-solving environment for validating scientific software
Numerical validation has become a major concern in many scientific applications. This paper prese... more Numerical validation has become a major concern in many scientific applications. This paper presents the software environment Aquarels which integrates through a window-based interface various tools to tackle numerical validation. Aquarels includes tools to control floating-point arithmetic, perturbation tools, interval arithmetic, multi-precision arithmetic. Several real-life applications illustrate the efficiency of this software.
Computation of the Singular Subspace Associated With the Smallest Singular Values of Large Matrices
: We compare the block-Lanczos and the Davidson methods for computing a basis of a singular subsp... more : We compare the block-Lanczos and the Davidson methods for computing a basis of a singular subspace associated with the smallest singular values of large matrices. We introduce a simple modification on the preconditioning step of Davidson's method which appears to be efficient on a range of large sparse matrices. Key-words: Block-Lanczos method, Davidson's method, SVD, preconditioning, sparse matrices. (R'esum'e : tsvp) Centre National de la Recherche Scientifique Institut National de Recherche en Informatique (URA 227) Universit e de Rennes 1 -- Insa de Rennes et en Automatique -- unit e de recherche de Rennes Calcul du sous espace singulier associ'e aux plus petites valeurs singuli`eres de matrices creuses de grande taille R'esum'e : Nous comparons la m'ethode de Lanczos par blocs et la m'ethode de Davidson pour calculer le sous-espace singulier associ'e aux plus petites valeurs singuli`eres de matrices creuses de grande taille. Nous introd...
Numerical methods related on Krylov subspaces are widely used in large sparse numerical linear al... more Numerical methods related on Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated through their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. Unfortunately, this technique is rather inflexible to be efficiently implemented on parallel computers. In this report we examine several parallel and stable algorithms based on the idea of Reichel et al. which retrieve at their completion the same information as the sequential Arnoldi's method. We present timing results obtained from their implementations on the Intel Paragon distributed-memory multiprocessor machine. (Résumé d'auteur)
Electronic transactions on numerical analysis ETNA
A procedure for counting the number of eigenvalues of a matrix in a region surrounded by a closed... more A procedure for counting the number of eigenvalues of a matrix in a region surrounded by a closed curve is presented. It is based on the application of the residual theorem. The quadrature is performed by evaluating the principal argument of the logarithm of a function. A strategy is proposed for selecting a path length that insures that the same branch of the logarithm is followed during the integration. Numerical tests are reported for matrices obtained from conventional matrix test sets.
Diierent parallel algorithms are designed and evaluated for computing the multipli-cation of a ve... more Diierent parallel algorithms are designed and evaluated for computing the multipli-cation of a vector by a Kronecker tensor product of elementary matrices. The algorithms are based on an analytic computation model together with some algebraic properties of the Kronecker multi-plication. From that theoretical study, t wo algorithms are proposed which diier on the volume of oating-point operations and communication they involve. A special study of the data and comput-ing distribution is proposed depending on the dimensions of the elementary matrices. Experimental results show the eeciency of the approach.
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Papers by Bernard Philippe