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SOLVING SPARSE TRIANGULAR LINEAR SYSTEMS ON PARALLEL COMPUTERS

1989
*
International journal of high speed computing
*

Fortunately, though, the structure of the

doi:10.1142/s0129053389000056
fatcat:pqjsiyvz3zbnniienbqzcuj6t4
*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*. ...##
###
The Parallel Solution Method of Sparse Triangular System Based on Correlation Decomposition

2018
*
DEStech Transactions on Computer Science and Engineering
*

We propose a

doi:10.12783/dtcse/iece2018/26645
fatcat:zjxidmxazfgr3h3zqhgcqrl5nq
*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*. ...##
###
Parallel algorithms for forward and back substitution in direct solution of sparse linear systems

1995
*
Proceedings of the 1995 ACM/IEEE conference on Supercomputing (CDROM) - Supercomputing '95
*

A few

doi:10.1145/224170.224471
dblp:conf/sc/GuptaK95
fatcat:nfqpljy7wredncqddhmq44s2xm
*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*. ...##
###
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

doi:10.21172/ijiet.91.08
fatcat:kl5ckzmwh5b2bgug5kmz5nmhse
*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). ...##
###
Accelerating the GMRES Solver with Block ILU (K) Preconditioner on GPUs in Reservoir Simulation

2015
*
Journal of Geology & Geosciences
*

In this paper,

doi:10.4172/2329-6755.1000199
fatcat:kwi7pcfg3beirjqjorowabpafa
*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*. ...##
###
Iterative Sparse Triangular Solves for Preconditioning
[chapter]

2015
*
Lecture Notes in Computer Science
*

We demonstrate the performance gains that this approach can have

doi:10.1007/978-3-662-48096-0_50
fatcat:k4p5ysqnhza3djruia4kvsc5j4
*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. ...##
###
A Hybrid Approach for Parallel Transistor-Level Full-Chip Circuit Simulation
[chapter]

2015
*
Lecture Notes in Computer Science
*

This approach focuses

doi:10.1007/978-3-319-17353-5_9
fatcat:5jrocvi2b5cltcfgjwkc6gs6by
*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*. ...##
###
Direct Linear Solvers for Vector and Parallel Computers
[chapter]

1999
*
Lecture Notes in Computer Science
*

For

doi:10.1007/10703040_10
fatcat:6pjposooxfdeziv4kaf7ryk6qy
*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*. ...##
###
GPU-accelerated preconditioned iterative linear solvers

2012
*
Journal of Supercomputing
*

Our goal is to illustrate the advantages and difficulties encountered when deploying GPU technology to perform

doi:10.1007/s11227-012-0825-3
fatcat:cc6x2cxrbbe5tlqujevezdjm4q
*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] . ...##
###
Parallel Implementation of LQG Balanced Truncation for Large-Scale Systems
[chapter]

2008
*
Lecture Notes in Computer Science
*

Numerical examples

doi:10.1007/978-3-540-78827-0_24
fatcat:uzmymuxsmfdulgk64xswpty3we
*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*. ...##
###
Parallel computation of a Krylov matrix for a sparse and structured input

1995
*
Mathematical and computer modelling
*

As in our previous work, we reduce

doi:10.1016/0895-7177(95)00084-f
fatcat:2rv2mevjanbnrkqxwtyigwrnlm
*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. ...##
###
On Parallel Solution of Sparse Triangular Linear Systems in CUDA
[article]

2017
*
arXiv
*
pre-print

However, the development of efficient

arXiv:1710.04985v1
fatcat:sydqdpsosjblbc64itdmjlkpde
*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. ...##
###
Equal bi-Vectorized (EBV) method to high performance on GPU
[article]

2019
*
arXiv
*
pre-print

Due to importance of reducing of time solution in numerical codes, we propose an algorithm for

arXiv:1907.05767v1
fatcat:qe4obdtutnhmfgm6qdsqhermii
*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. ...##
###
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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