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SOLVING SPARSE TRIANGULAR LINEAR SYSTEMS ON PARALLEL COMPUTERS

EDWARD ANDERSON, YOUCEF SAAD
1989 International journal of high speed computing  
Fortunately, though, the structure of the Computer Science Ph.D. program at CMU is such that I was given time to overcome these difficulties.  ...  The list is far too long to detail here, but I would especially like to thank Doug Reece for all the time spent listening to my troubles on long runs through Schenley Park.  ...  Sparse linear systems are often solved using different computational techniques than those employed to solve dense systems.  ... 
doi:10.1142/s0129053389000056 fatcat:pqjsiyvz3zbnniienbqzcuj6t4

The Parallel Solution Method of Sparse Triangular System Based on Correlation Decomposition

Li-cui SONG, Song JIN, Tian-cheng LV
2018 DEStech Transactions on Computer Science and Engineering  
We propose a parallel solution algorithm based on correlation decomposition.  ...  By decomposing the right-hand-side of the linear system and analyzing the dependencies of the variable solution to form multiple independent variable calculation paths.  ...  sparse linear triangular systems.  ... 
doi:10.12783/dtcse/iece2018/26645 fatcat:zjxidmxazfgr3h3zqhgcqrl5nq

Parallel algorithms for forward and back substitution in direct solution of sparse linear systems

Anshul Gupta, Vipin Kumar
1995 Proceedings of the 1995 ACM/IEEE conference on Supercomputing (CDROM) - Supercomputing '95  
A few parallel algorithms for solving triangular systems resulting from parallel factorization of sparse linear systems have been proposed and implemented recently.  ...  It has been a common belief that parallel sparse triangular solvers are quite unscalable due to a high communication to computation ratio.  ...  Solving a triangular system corresponding to this supernode involves asymptotically a computation of the same complexity as solving the entire sparse triangular system.  ... 
doi:10.1145/224170.224471 dblp:conf/sc/GuptaK95 fatcat:nfqpljy7wredncqddhmq44s2xm

Page 6624 of Mathematical Reviews Vol. , Issue 90K [page]

1990 Mathematical Reviews  
Parallel Comput. 11 (1989), no. 2, 201-221. Summary: “Parallel algorithms for triangularization of large, sparse, and unsymmetric matrices are presented.  ...  UNSYMMLQ method for solving large-scale nonsymmetric linear systems.  ... 

Solving System of Linear Equations in Parallel using Multithread

2017 International Journal of Innovations in Engineering and Technology  
This paper deals with the efficient parallel algorithms for solving linear equations using multithread. Since using Multi thread, each thread represent one processor, execution time is minimized.  ...  Finally we conclude that the parallel algorithm performance better than the sequential algorithm.  ...  Scalable Parallel Algorithms for solving sparse Systems of Linear Equations was done by Anshul Gupta (1998).  ... 
doi:10.21172/ijiet.91.08 fatcat:kl5ckzmwh5b2bgug5kmz5nmhse

Accelerating the GMRES Solver with Block ILU (K) Preconditioner on GPUs in Reservoir Simulation

Hui Liu Bo Yang
2015 Journal of Geology & Geosciences  
In this paper, parallel solution techniques for block triangular systems are proposed, which work for matrices with an arbitrary block size.  ...  This paper studies the parallelization of the restarted GMRES solver, GMRES (m), and the block ILU (k) preconditioner on GPUs used in petroleum reservoir simulations.  ...  Solution for block triangular systems on GPUs When implementing equation (6) , a lower triangular linear system, Lx = b, and an upper triangular linear system, U x = b, are required to solve.  ... 
doi:10.4172/2329-6755.1000199 fatcat:kwi7pcfg3beirjqjorowabpafa

Iterative Sparse Triangular Solves for Preconditioning [chapter]

Hartwig Anzt, Edmond Chow, Jack Dongarra
2015 Lecture Notes in Computer Science  
We demonstrate the performance gains that this approach can have on GPUs in the context of solving sparse linear systems with a preconditioned Krylov subspace method.  ...  We propose using an iterative approach for solving sparse triangular systems when an approximation is suitable.  ...  Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Numbers DE-SC-0012538 and DE-SC-0010042.  ... 
doi:10.1007/978-3-662-48096-0_50 fatcat:k4p5ysqnhza3djruia4kvsc5j4

A Hybrid Approach for Parallel Transistor-Level Full-Chip Circuit Simulation [chapter]

Heidi K. Thornquist, Sivasankaran Rajamanickam
2015 Lecture Notes in Computer Science  
This approach focuses on the computationally expensive part of the simulator: the linear system solve.  ...  Hybrid versions of two iterative linear solver strategies are presented, one takes advantage of block triangular form structure while the other uses a Schur complement technique.  ...  The hybrid Schur approximation uses a triangular solve with multiple righthand sides to compute a block column of the Schur complement in parallel.  ... 
doi:10.1007/978-3-319-17353-5_9 fatcat:5jrocvi2b5cltcfgjwkc6gs6by

Direct Linear Solvers for Vector and Parallel Computers [chapter]

Friedrich Grund
1999 Lecture Notes in Computer Science  
For solving several linear systems with the same pattern structure we generate a pseudo code, that can be interpreted repeatedly to compute the solutions of these systems.  ...  We consider direct methods for the numerical solution of linear systems with unsymmetric sparse matrices. Di erent strategies for the determination of the pivots are studied.  ...  Here, the linear systems have been solved on the parallel computer while the other parts of the algorithms of SPEEDUP have been performed on the vector computer.  ... 
doi:10.1007/10703040_10 fatcat:6pjposooxfdeziv4kaf7ryk6qy

GPU-accelerated preconditioned iterative linear solvers

Ruipeng Li, Yousef Saad
2012 Journal of Supercomputing  
Our goal is to illustrate the advantages and difficulties encountered when deploying GPU technology to perform sparse linear algebra computations.  ...  Our experiments with an NVIDIA TESLA C1060 show that for unstructured matrices SpMV kernels can be up to 10 times faster on the GPU than on the host Intel Xeon E5504 Processor.  ...  The Block-ILU preconditioned GMRES method is studied for solving sparse linear systems on the NVIDIA Tesla GPUs in [27] .  ... 
doi:10.1007/s11227-012-0825-3 fatcat:cc6x2cxrbbe5tlqujevezdjm4q

Parallel Implementation of LQG Balanced Truncation for Large-Scale Systems [chapter]

Jose M. Badía, Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, Alfredo Remón
2008 Lecture Notes in Computer Science  
Numerical examples on a parallel computer demonstrate the effectiveness of our approach.  ...  Model reduction of large-scale linear time-invariant systems is an ubiquitous task in control and simulation of complex dynamical processes.  ...  Concluding Remarks We have provided evidence in support of the benefits of the LQG BT method for model reduction of large-scale systems.  ... 
doi:10.1007/978-3-540-78827-0_24 fatcat:uzmymuxsmfdulgk64xswpty3we

Parallel computation of a Krylov matrix for a sparse and structured input

V.Y. Pan
1995 Mathematical and computer modelling  
As in our previous work, we reduce parallel computation of a Krylov matrix to solving a parametrized linear system of equations.  ...  This time we show that such a method is effective in the cases of banded matrices, sparse and structured matrices and triangular matrices.  ...  In this case, application of the parallel generalized nested dissection algorithm of [9] gives the cost bound O(log3 n, (s(n)d)/ log2 n) f or solving a linear system with scalar sparse input matrix.  ... 
doi:10.1016/0895-7177(95)00084-f fatcat:2rv2mevjanbnrkqxwtyigwrnlm

On Parallel Solution of Sparse Triangular Linear Systems in CUDA [article]

Ruipeng Li
2017 arXiv   pre-print
However, the development of efficient parallel algorithms in CUDA for solving sparse triangular linear systems remains a challenging task due to the inherently sequential nature of the computation.  ...  Solving linear systems with sparse triangular structured matrices is another important sparse kernel as demanded by a variety of scientific and engineering applications such as sparse linear solvers.  ...  The author acknowledges fruitful discussions with Weifeng Liu on their global-synchronization-free SpTrSv algorithms.  ... 
arXiv:1710.04985v1 fatcat:sydqdpsosjblbc64itdmjlkpde

Equal bi-Vectorized (EBV) method to high performance on GPU [article]

Amirreza Hashemi, Mohsen Lahooti, Ebrahim Shirani
2019 arXiv   pre-print
Due to importance of reducing of time solution in numerical codes, we propose an algorithm for parallel LU decomposition solver for dense and sparse matrices on GPU.  ...  This algorithm is based on first bi-vectorizing a triangular matrices of decomposed coefficient matrix and then equalizing vectors.  ...  Acknowledgment Authors would like to acknowledge the CFD group of Isfahan University of Technology for providing computational platforms for all of tests.  ... 
arXiv:1907.05767v1 fatcat:qe4obdtutnhmfgm6qdsqhermii

Page 7619 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
Summary: “In this paper we survey a recent approach for solving sparse triangular systems of equations on highly parallel comput- ers.  ...  sparse linear systems.  ... 
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