The Experts below are selected from a list of 10026 Experts worldwide ranked by ideXlab platform
Roberto Guerrieri - One of the best experts on this subject based on the ideXlab platform.
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Triangular Matrix Inversion on Heterogeneous Multicore Systems
IEEE Transactions on Parallel and Distributed Systems, 2012Co-Authors: Florian Ries, Tommaso De Marco, Roberto GuerrieriAbstract:Dense Matrix inversion is a basic procedure in many linear algebra algorithms. Any factorization-based dense Matrix inversion algorithm involves the inversion of one or two Triangular matrices. In this work, we present an improved implementation of a parallel Triangular Matrix inversion for heterogeneous multicore CPU/dual-GPU systems.
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Triangular Matrix inversion on Graphics Processing Unit
Proceedings of the Conference on High Performance Computing Networking Storage and Analysis, 2009Co-Authors: Florian Ries, Tommaso De Marco, Matteo Zivieri, Roberto GuerrieriAbstract:Dense Matrix inversion is a basic procedure in many linear algebra algorithms. A computationally arduous step in most dense Matrix inversion methods is the inversion of Triangular matrices as produced by factorization methods such as LU decomposition. In this paper, we demonstrate how Triangular Matrix inversion (TMI) can be accelerated considerably by using commercial Graphics Processing Units (GPU) in a standard PC. Our implementation is based on a divide and conquer type recursive TMI algorithm, efficiently adapted to the GPU architecture. Our implementation obtains a speedup of 34x versus a CPU-based LAPACK reference routine, and runs at up to 54 gigaflops/s on a GTX 280 in double precision. Limitations of the algorithm are discussed, and strategies to cope with them are introduced. In addition, we show how inversion of an L- and U-Matrix can be performed concurrently on a GTX 295 based dual-GPU system at up to 90 gigaflops/s.
Florian Ries - One of the best experts on this subject based on the ideXlab platform.
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Triangular Matrix Inversion on Heterogeneous Multicore Systems
IEEE Transactions on Parallel and Distributed Systems, 2012Co-Authors: Florian Ries, Tommaso De Marco, Roberto GuerrieriAbstract:Dense Matrix inversion is a basic procedure in many linear algebra algorithms. Any factorization-based dense Matrix inversion algorithm involves the inversion of one or two Triangular matrices. In this work, we present an improved implementation of a parallel Triangular Matrix inversion for heterogeneous multicore CPU/dual-GPU systems.
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Triangular Matrix inversion on Graphics Processing Unit
Proceedings of the Conference on High Performance Computing Networking Storage and Analysis, 2009Co-Authors: Florian Ries, Tommaso De Marco, Matteo Zivieri, Roberto GuerrieriAbstract:Dense Matrix inversion is a basic procedure in many linear algebra algorithms. A computationally arduous step in most dense Matrix inversion methods is the inversion of Triangular matrices as produced by factorization methods such as LU decomposition. In this paper, we demonstrate how Triangular Matrix inversion (TMI) can be accelerated considerably by using commercial Graphics Processing Units (GPU) in a standard PC. Our implementation is based on a divide and conquer type recursive TMI algorithm, efficiently adapted to the GPU architecture. Our implementation obtains a speedup of 34x versus a CPU-based LAPACK reference routine, and runs at up to 54 gigaflops/s on a GTX 280 in double precision. Limitations of the algorithm are discussed, and strategies to cope with them are introduced. In addition, we show how inversion of an L- and U-Matrix can be performed concurrently on a GTX 295 based dual-GPU system at up to 90 gigaflops/s.
Jae Keol Park - One of the best experts on this subject based on the ideXlab platform.
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Triangular Matrix Representations and Triangular Matrix Extensions
Extensions of Rings and Modules, 2020Co-Authors: Gary F Birkenmeier, Jae Keol Park, S. Tariq RizviAbstract:In this chapter, generalized Triangular Matrix representations are discussed by introducing the concept of a set of left triangulating idempotents. A criterion for a ring with a complete set of triangulating idempotents to be quasi-Baer is provided. A structure theorem for a quasi-Baer ring with a complete set of triangulating idempotents is shown using complete Triangular Matrix representations. A number of well known results follow as consequences of this useful structure theorem. The results which follow as a consequence include Levy’s decomposition theorem of semiprime right Goldie rings, Faith’s characterization of semiprime right FPF rings with no infinite set of central orthogonal idempotents, Gordon and Small’s characterization of piecewise domains, and Chatters’ decomposition theorem of hereditary noetherian rings. A result related to Michler’s splitting theorem for right hereditary right noetherian rings is also obtained as an application. The Baer, the quasi-Baer, the FI-extending, and the strongly FI-extending properties of (generalized) Triangular Matrix rings are discussed. A sheaf representation of quasi-Baer rings is obtained as an application of the results of this chapter.
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Triangular Matrix representations of ring extensions
Journal of Algebra, 2003Co-Authors: Gary F Birkenmeier, Jae Keol ParkAbstract:In this paper we investigate the class of piecewise prime, PWP, rings which properly includes all piecewise domains (hence all right hereditary rings which are semiprimary or right Noetherian). For a PWP ring we determine a large class of ring extensions which have a generalized Triangular Matrix representation for which the diagonal rings are prime.
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generalized Triangular Matrix rings and the fully invariant extending property
Rocky Mountain Journal of Mathematics, 2002Co-Authors: Gary F Birkenmeier, Jae Keol Park, Tariq S RizviAbstract:A module M is called (strongly) FI-extending if every fully invariant submodule of M is essential in a (fully invariant) direct summand of M. A ring R with unity is called quasi-Baer if the right annihilator of every ideal is generated, as a right ideal, by an idempotent. For semi-prime rings the FI-extending condition, strongly FI-extending condition and quasi-Baer condition are equivalent. In this paper we fully characterize the 2-by-2 generalized (or formal) Triangular Matrix rings which are either (right) FI-extending, (right) strongly FI-extending, or quasi-Baer. Examples are provided to illustrate and delimit our results.
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Triangular Matrix REPRESENTATIONS OF SEMIPRIMARY RINGS
Journal of Algebra and Its Applications, 2002Co-Authors: Gary F Birkenmeier, Jae Keol ParkAbstract:In this paper we characterize internally a TSA ring (i.e. a generalized Triangular Matrix ring with simple Artinian rings on the diagonal) in terms of its prime ideals. Also we show that the class of semiprimary quasi-Baer rings is a proper subclass of the class of TSA rings. Moreover, we generalize results of Harada, Small, and Teply on semiprimary rings. Finally we prove that under certain cardinality conditions a semiprimary quasi-Baer ring becomes semisimple Artinian.
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Triangular Matrix representations
Journal of Algebra, 2000Co-Authors: Gary F Birkenmeier, Henry E Heatherly, Jae Keol ParkAbstract:In this paper we develop the theory of generalized Triangular Matrix representation in an abstract setting. This is accomplished by introducing the concept of a set of left triangulating idempotents. These idempotents determine a generalized Triangular Matrix representation for an algebra. The existence of a set of left triangulating idempotents does not depend on any specific conditions on the algebras; however, if the algebra satisfies a mild finiteness condition, then such a set can be refined to a “complete” set of left triangulating idempotents in which each “diagonal” subalgebra has no nontrivial generalized Triangular Matrix representation. We then apply our theory to obtain new results on generalized Triangular Matrix representations, including extensions of several well known results.
Yu Wang - One of the best experts on this subject based on the ideXlab platform.
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The images of multilinear polynomials on 2 × 2 upper Triangular Matrix algebras
Linear & Multilinear Algebra, 2019Co-Authors: Yu WangAbstract:ABSTRACTThe purpose of this paper is to give a correct proof of a result on the images of non-commutative multilinear polynomials on 2×2 upper Triangular Matrix algebra.
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Functional identities in upper Triangular Matrix rings revisited
Linear & Multilinear Algebra, 2017Co-Authors: Yu WangAbstract:AbstractThe aim of this paper is to give an improvement of a result on functional identities in upper Triangular Matrix rings obtained by Eremita, which presents a short proof of Eremita’s result.
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Jordan homomorphisms of upper Triangular Matrix rings over a prime ring
Linear Algebra and its Applications, 2014Co-Authors: Yiqiu Du, Yu WangAbstract:Abstract The aim of the paper is to prove that under a mild assumption every Jordan homomorphism from an upper Triangular Matrix ring over a unital ring onto another upper Triangular Matrix ring over a unital prime ring of characteristic not 2 is either a homomorphism or an anti-homomorphism. This result is an extension of a classical theorem of Herstein.
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jordan homomorphisms of upper Triangular Matrix rings
Linear Algebra and its Applications, 2013Co-Authors: Yao Wang, Yu WangAbstract:Abstract In this paper we investigate Jordan homomorphisms of upper Triangular Matrix rings and give a sufficient condition under which they are necessarily homomorphisms or anti-homomorphisms.
Xiaowu Chen - One of the best experts on this subject based on the ideXlab platform.
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singularity categories schur functors and Triangular Matrix rings
arXiv: Representation Theory, 2007Co-Authors: Xiaowu ChenAbstract:We study certain Schur functors which preserve singularity categories of rings and we apply them to study the singularity category of Triangular Matrix rings. In particular, combining these results with Buchweitz-Happel's theorem, we can describe singularity categories of certain non-Gorenstein rings via the stable category of maximal Cohen-Macaulay modules. Three concrete examples of finite-dimensional algebras with the same singularity category are discussed.
