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Journal articles on the topic 'Sparse Basic Linear Algebra Subroutines'

Author: Grafiati

Published: 6 September 2023

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1

Yang, Bing, Xi Chen, Xiang Yun Liao, Mian Lun Zheng, and Zhi Yong Yuan. "FEM-Based Modeling and Deformation of Soft Tissue Accelerated by CUSPARSE and CUBLAS." Advanced Materials Research 671-674 (March 2013): 3200–3203. http://dx.doi.org/10.4028/www.scientific.net/amr.671-674.3200.

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Realistic modeling and deformation of soft tissue is one of the key technologies of virtual surgery simulation which is a challenging research field that stimulates the development of new clinical applications such as the virtual surgery simulator. In this paper we adopt the linear FEM (Finite Element Method) and sparse matrix compression stored in CSR (Compressed Sparse Row) format that enables fast modeling and deformation of soft tissue on GPU hardware with NVIDIA’s CUSPARSE (Compute Unified Device Architecture Sparse Matrix) and CUBLAS (Compute Unified Device Architecture Basic Linear Alge

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2

Magnin, H., and J. L. Coulomb. "A parallel and vectorial implementation of basic linear algebra subroutines in iterative solving of large sparse linear systems of equations." IEEE Transactions on Magnetics 25, no. 4 (1989): 2895–97. http://dx.doi.org/10.1109/20.34317.

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3

Kramer, David, S. Lennart Johnsson, and Yu Hu. "Local Basic Linear Algebra Subroutines (LBLAS) for the CM-5/5E." International Journal of Supercomputer Applications and High Performance Computing 10, no. 4 (1996): 300–335. http://dx.doi.org/10.1177/109434209601000403.

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4

Shaeffer, John. "BLAS IV: A BLAS for Rk Matrix Algebra." Applied Computational Electromagnetics Society 35, no. 11 (2021): 1266–67. http://dx.doi.org/10.47037/2020.aces.j.351102.

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Basic Linear Algebra Subroutines (BLAS) are well-known low-level workhorse subroutines for linear algebra vector-vector, matrixvector and matrix-matrix operations for full rank matrices. The advent of block low rank (Rk) full wave direct solvers, where most blocks of the system matrix are Rk, an extension to the BLAS III matrix-matrix work horse routine is needed due to the agony of Rk addition. This note outlines the problem of BLAS III for Rk LU and solve operations and then outlines an alternative approach, which we will call BLAS IV. This approach utilizes the thrill of Rk matrix-matrix mu

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5

Demmel, James W., Michael T. Heath, and Henk A. van der Vorst. "Parallel numerical linear algebra." Acta Numerica 2 (January 1993): 111–97. http://dx.doi.org/10.1017/s096249290000235x.

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We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of paralled processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illustrate these principles using current architectures and software systems, and by showing how one would implement matrix multiplication. Then, we present direct and iterative algorithms for solving linear systems of equations, linear least squares problems, the symmetric eigenvalue problem, the nonsymm

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6

Duff, Iain S., Michele Marrone, Giuseppe Radicati, and Carlo Vittoli. "Level 3 basic linear algebra subprograms for sparse matrices." ACM Transactions on Mathematical Software 23, no. 3 (1997): 379–401. http://dx.doi.org/10.1145/275323.275327.

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7

Dodson, David S., Roger G. Grimes, and John G. Lewis. "Sparse extensions to the FORTRAN Basic Linear Algebra Subprograms." ACM Transactions on Mathematical Software 17, no. 2 (1991): 253–63. http://dx.doi.org/10.1145/108556.108577.

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8

Dodson, David S., and John G. Lewis. "Proposed sparse extensions to the Basic Linear Algebra Subprograms." ACM SIGNUM Newsletter 20, no. 1 (1985): 22–25. http://dx.doi.org/10.1145/1057935.1057938.

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9

Duff, Iain S., Michael A. Heroux, and Roldan Pozo. "An overview of the sparse basic linear algebra subprograms." ACM Transactions on Mathematical Software 28, no. 2 (2002): 239–67. http://dx.doi.org/10.1145/567806.567810.

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10

Aliaga, José I., Rocío Carratalá-Sáez, and Enrique S. Quintana-Ortí. "Parallel Solution of Hierarchical Symmetric Positive Definite Linear Systems." Applied Mathematics and Nonlinear Sciences 2, no. 1 (2017): 201–12. http://dx.doi.org/10.21042/amns.2017.1.00017.

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AbstractWe present a prototype task-parallel algorithm for the solution of hierarchical symmetric positive definite linear systems via the ℋ-Cholesky factorization that builds upon the parallel programming standards and associated runtimes for OpenMP and OmpSs. In contrast with previous efforts, our proposal decouples the numerical aspects of the linear algebra operation from the complexities associated with high performance computing. Our experiments make an exhaustive analysis of the efficiency attained by different parallelization approaches that exploit either task-parallelism or loop-para

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11

Johnsson, S. Lennart, and Luis F. Ortiz. "Local Basic Linear Algebra Subroutines (Lblas) for Distributed Memory Architectures and Languages With Array Syntax." International Journal of Supercomputing Applications 6, no. 4 (1992): 322–50. http://dx.doi.org/10.1177/109434209200600403.

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12

Dodson, David S., Roger G. Grimes, and John G. Lewis. "Algorithm 692: Model implementation and test package for the Sparse Basic Linear Algebra Subprograms." ACM Transactions on Mathematical Software 17, no. 2 (1991): 264–72. http://dx.doi.org/10.1145/108556.108582.

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13

Vuik, C. "Krylov Subspace Solvers and Preconditioners." ESAIM: Proceedings and Surveys 63 (2018): 1–43. http://dx.doi.org/10.1051/proc/201863001.

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In these lecture notes an introduction to Krylov subspace solvers and preconditioners is presented. After a discretization of partial differential equations large, sparse systems of linear equations have to be solved. Fast solution of these systems is very urgent nowadays. The size of the problems can be 1013 unknowns and 1013 equations. Iterative solution methods are the methods of choice for these large linear systems. We start with a short introduction of Basic Iterative Methods. Thereafter preconditioned Krylov subspace methods, which are state of the art, are describeed. A distinction is

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14

Morris, Karla, Damian W. I. Rouson, M. Nicole Lemaster, and Salvatore Filippone. "Exploring Capabilities within ForTrilinos by Solving the 3D Burgers Equation." Scientific Programming 20, no. 3 (2012): 275–92. http://dx.doi.org/10.1155/2012/378791.

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We present the first three-dimensional, partial differential equation solver to be built atop the recently released, open-source ForTrilinos package (http://trilinos.sandia.gov/packages/fortrilinos). ForTrilinos currently provides portable, object-oriented Fortran 2003 interfaces to the C++ packages Epetra, AztecOO and Pliris in the Trilinos library and framework [ACM Trans. Math. Softw.31(3) (2005), 397–423]. Epetra provides distributed matrix and vector storage and basic linear algebra calculations. Pliris provides direct solvers for dense linear systems. AztecOO provides iterative sparse li

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15

Egunov, V. A., and A. G. Kravets. "A Method for Improving the Caching Strategy for Computing Systems with Shared Memory." Programmnaya Ingeneria 14, no. 7 (2023): 329–38. http://dx.doi.org/10.17587/prin.14.329-338.

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This paper considers the problem of increasing the software efficiency in terms of reducing the costs of their development and operation in the process of solving production and research tasks. We have analysed the existing approaches to solving this problem by example of parameterized algorithms for implementing mVm (matrix—vector multiplication) and MMM (matrix—matrix multiplication)) BLAS (Basic Linear Algebra Subroutines) operations. To achieve the goal of increasing the software efficiency, we proposed a new design method, designed to improve data caching algorithms in the software develo

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16

Stringer, James C., L. Kent Thomas, and Ray G. Pierson. "Efficiency of D4 Gaussian Elimination on a Vector Computer." Society of Petroleum Engineers Journal 25, no. 01 (1985): 121–24. http://dx.doi.org/10.2118/11082-pa.

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Abstract The efficiency of D4 Gaussian elimination on a vector computer, the Cray- 1/S, it examined. The algorithm used in this work is employed routinely in Phillips Petroleum Co. reservoir simulation models. Comparisons of scalar Phillips Petroleum Co. reservoir simulation models. Comparisons of scalar and vector Cray-1/S times are given for various example cases including multiple unknowns per gridblock. Vectorization of the program on the Cray- 1/S is discussed. Introduction In reservoir simulation, the solution of large systems of linear equations accounts for a substantial percentage of

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17

Zhao, Liming, Zhikuan Zhao, Patrick Rebentrost, and Joseph Fitzsimons. "Compiling basic linear algebra subroutines for quantum computers." Quantum Machine Intelligence 3, no. 2 (2021). http://dx.doi.org/10.1007/s42484-021-00048-8.

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18

Šimeček, I. "Acceleration of Sparse Matrix-Vector Multiplication by Region Traversal." Acta Polytechnica 48, no. 4 (2008). http://dx.doi.org/10.14311/1029.

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Sparse matrix-vector multiplication (shortly SpM×V) is one of most common subroutines in numerical linear algebra. The problem is that the memory access patterns during SpM×V are irregular, and utilization of the cache can suffer from low spatial or temporal locality. Approaches to improve the performance of SpM×V are based on matrix reordering and register blocking. These matrix transformations are designed to handle randomly occurring dense blocks in a sparse matrix. The efficiency of these transformations depends strongly on the presence of suitable blocks. The overhead of reorganization of

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