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Relevant bibliographies by topics / Sparse Basic Linear Algebra Subroutines

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Academic literature on the topic 'Sparse Basic Linear Algebra Subroutines'

Author: Grafiati

Published: 6 September 2023

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

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 Algebra Subroutines) library. We focus on the CGS (Conjugate Gradient Solver) which is the mainly time-consuming part of FEM, and transplant it onto GPU with the two libraries mentioned above. The experimental results show that the accelerating method in this paper can achieve realistic and fast modeling and deformation simulation of soft tissue.

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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 multiply and uses the Adaptive Cross Approximation (ACA) as a methodology to evaluate sums of Rk terms to circumvent the agony of low rank addition.

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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 nonsymmetric eigenvalue problem, and the singular value decomposition. We consider dense, band and sparse matrices.

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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-parallelism via a runtime. Alternatively, we also evaluate a solution that leverages multi-threaded parallelism via the parallel implementation of the Basic Linear Algebra Subroutines (BLAS) in Intel MKL.

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