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Block Iterators for Sparse Matrices

2016
*
Proceedings of the 2016 Federated Conference on Computer Science and Information Systems
*

Finding an optimal

doi:10.15439/2016f35
dblp:conf/fedcsis/LangrSD16
fatcat:s5hc4quiqvhufgjacvcwm26mdu
*block*size*for*a given*sparse*matrix forms an important problem*for*storage formats that partition*matrices*into uniformly-sized*blocks*. ... A key*for*an efficient solution is the ability to quickly*iterate*,*for*a particular*block*size, over matrix nonzero*blocks*. ... Václavík of the Czech Technical University in Prague*for*providing an access to an Intel Xeon Phi accelerator installed at the Star university cluster. ...##
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Iterative Sparse Triangular Solves for Preconditioning
[chapter]

2015
*
Lecture Notes in Computer Science
*

We propose using an

doi:10.1007/978-3-662-48096-0_50
fatcat:k4p5ysqnhza3djruia4kvsc5j4
*iterative*approach*for*solving*sparse*triangular systems when an approximation is suitable. ... This approach will not work*for*all problems, but can be successful*for**sparse*triangular*matrices*arising from incomplete factorizations, where an approximate solution is acceptable. ... Thus, although Jacobi*iterations*will not work*for*all*matrices*, there are large, useful classes of*matrices**for*which Jacobi*iterations*can be a viable approach*for*solving*sparse*triangular systems. ...##
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Scalable task-based algorithm for multiplication of block-rank-sparse matrices

2015
*
Proceedings of the 5th Workshop on Irregular Applications Architectures and Algorithms - IA3 '15
*

inverse of

doi:10.1145/2833179.2833186
dblp:conf/sc/CalvinLV15
fatcat:u2cikz45ozgptkp4i7ywlhpnqe
*block*-rank-*sparse*QC*matrices*is demonstrated;*for*full-rank (dense)*matrices*the performance of our SUMMA formulation usually exceeds that of the state-of-the-art dense MM implementations ...*matrices*that appear in the domain of quantum chemistry (QC). ... MM of two*matrices*with full-rank and rank-*sparse**blocks*will lead to*block*MMs and*block*additions operations having mixed rank-*sparse*and full-rank representations. ...##
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A hardware acceleration technique for gradient descent and conjugate gradient

2011
*
2011 IEEE 9th Symposium on Application Specific Processors (SASP)
*

Unlike traditional accelerators, our design accelerates different types of linear algebra operations found in many algorithms and is capable of efficiently handling

doi:10.1109/sasp.2011.5941086
dblp:conf/sasp/KeslerDK11
fatcat:o4ahplwirnfoxmvnoiabza2m2a
*sparse**matrices*that arise in applications ... We show that the proposed accelerator can provide significant speedups*for**iterative*versions of several applications and that*for*some applications such as least squares, it can substantially improve ... ACKNOWLEDGEMENTS The authors would like to thank Joseph Sloan and the anonymous referees*for*their valuable feedback. This work was supported in part by NSF and GSRC. ...##
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Conjugate Gradient and Lanczos Methods for Sparse Matrices on Distributed Memory Multiprocessors

1997
*
Journal of Parallel and Distributed Computing
*

coefficient

doi:10.1006/jpdc.1997.1364
fatcat:zcblw62k4zbebid7az2sgnuh7i
*matrices*-are crucial*for*an efficient execution. ... When these*iterative*solvers are parallelized on a multiprocessor system with distributed memory, the data distribution and the communication scheme -depending on the data structures used*for*the*sparse*... When*iterative*solvers are parallelized on a multiprocessor system with distributed memory, the data distribution and the communication scheme -depending on the data structures used*for**sparse**matrices*...##
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Some results on sparse block factorization iterative methods

1991
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Linear Algebra and its Applications
*

We consider the general

doi:10.1016/0024-3795(91)90295-8
fatcat:lkztrgrgrfaqxdikxkvoujbgxq
*sparse**block*factorization*iterative*methods as Beauwens and Ben Bouzid did. We develop some existence and convergence theorems*for*general nonsingular H-*matrices*. ... INTRODIJCTION Consider the linear system Ax = b, ( 1 1.1 where A is a nonsingular large*sparse*complex matrix. A conjugate gradient method to solve (1.1) has been proposed and studied in [2] and [3]. ... Meanwhile it produces automatically an*iterative*method*for*solving (l.l), the*sparse**block*factorization*iterative*method. 2,*SPARSE**BLOCK*FACTORIZATION*ITERATIVE*METHODS Let AEC"*" be partitioned ...##
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Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices

2000
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Applied Numerical Mathematics
*

We investigate the use of

doi:10.1016/s0168-9274(99)00047-1
fatcat:b65ckmqv5rcmjixyu7tteyij3q
*sparse*approximate inverse techniques in a multilevel*block*ILU preconditioner to design a robust and efficient parallelizable preconditioner*for*solving general*sparse**matrices*... Moreover, the new implementation of BILUM with a*sparse*approximate inverse strategy affords maximum parallelism*for*operations within each level as well as*for*the coarsest level solution. ... of size 100*for*solving the FIDAP*matrices**Matrices*Unknowns Nonzeros*iter*solu spar*iter*(BILUM) FIDAP004 1,601 32,287 27 1.05 6.95 2 FIDAP006 1,651 49,479 50 2.09 3.92 3 FIDAP020 ...##
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BLOCK MATRIX PRECONDITIONER METHOD FOR THE ELECTRIC FIELD INTEGRAL EQUATION (EFIE) FORMULATION BASED ON LOOP-STAR BASIS FUNCTIONS

2013
*
Electromagnetic Waves
*

Moreover, to improve the convergence rate of

doi:10.2528/pier12092403
fatcat:3qx3r75mybfv5d5mmxi2o4lxvq
*iterative*methods, a*block*matrix preconditioner (BMP) is applied to the EFIE formulation based on loop star-basis functions. ... Because the matrix system resulting from the conventional method of moments is a dense matrix, a*sparse*matrix version of each*block*matrix is constructed, followed by the inversion of the resultant*block*... is least chosen because the off-diagonal*block**matrices*have the weak coupling compared to the Z LL and Z SS*block**matrices*. ...##
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Sparse Matrices in Matlab*P: Design and Implementation
[chapter]

2004
*
Lecture Notes in Computer Science
*

Matlab*P can store distributed

doi:10.1007/978-3-540-30474-6_20
fatcat:7qd2oi37dvewlo4qfp5fzjx7am
*matrices*in either full or*sparse*format. As in Matlab, most matrix operations apply equally to full or*sparse*operands. ... Government is authorized to reproduce and distribute reprints*for*governmental purposes not withstanding any copyright notation thereon. ... The Matlab*P language allows*for**matrices*to be distributed by*block*rows or*block*columns. This is already the case*for*ddense*matrices*[?,7] . ...##
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Increasing the Locality of Iterative Methods and Its Application to the Simulation of Semiconductor Devices

2009
*
The international journal of high performance computing applications
*

In this paper a technique

doi:10.1177/1094342009106416
fatcat:ilvouiq345by3ioo4245ircqy4
*for*improving the locality of*sparse*matrix codes is presented. ... In these simulations the solution of large*sparse*linear equation systems is required, which are often solved using*iterative*methods. ...*For*example, register*blocking*only achieves good performance*for**matrices*with small dense-*blocks*in the pattern. ...##
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COMPARISONS OF THE PARALLEL PRECONDITIONERS FOR LARGE NONSYMMETRIC SPARSE LINEAR SYSTEMS ON A PARALLEL COMPUTER

2004
*
International journal of high speed computing
*

The results show that Multi-Color

doi:10.1142/s0129053304000232
fatcat:d33bmydqhvavdknmkzcmktp5vq
*Block*SOR and ILU(0) with Multi-Color ordering give the best performances*for*the finite difference*matrices*. ... Finally, we implemented the Multi-Color*Block*SOR preconditioner combined with direct*sparse*matrix solver. ...*For*the Multi-Color*Block*SOR method we used the MA48 package to invert the diagonal*block*. Multi-Color*Block*SOR(l) means that*Block*SOR was l times*iterated*. We used l = 2. ...##
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Task-Based Algorithm for Matrix Multiplication: A Step Towards Block-Sparse Tensor Computing
[article]

2015
*
arXiv
*
pre-print

These traits conflict with the irregular structure (

arXiv:1504.05046v1
fatcat:nid45r6nmbgctmgcw3t7xfbyt4
*block*-*sparse*or rank-*sparse*within*blocks*) that is increasingly relevant*for*fast methods in quantum physics. ...*For*square MM with uniform and nonuniform*block*sizes (the latter simulates*matrices*with general irregular structure) we found excellent performance in weak and strong-scaling regimes, on commodity and ... In other words, the*matrices*that we encounter are "*sparse*" in a general sense, which encompasses element,*block*, and*block*-level-rank sparsity; but in a practical sense the*matrices*are not*sparse*enough ...##
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Approximate Inverse Techniques for Block-Partitioned Matrices

1997
*
SIAM Journal on Scientific Computing
*

This paper proposes some preconditioning options when the system matrix is in

doi:10.1137/s1064827595281575
fatcat:wdbhfuzvyzb7vgvxhpfgxn7jzu
*block*-partitioned form. ... Approximate inverse techniques are used to generate*sparse*approximate solutions whenever these are needed in forming the preconditioner. ... 1 f in which both B and f are*sparse*. This is particularly the case*for**block*preconditioners*for**block*-tridiagonal*matrices*7, 19] . ...##
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Cross Low-Dimension Pursuit for Sparse Signal Recovery from Incomplete Measurements Based on Permuted Block Diagonal Matrix

2011
*
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
*

of the original signal from them in an

doi:10.1587/transfun.e94.a.1793
fatcat:pd4gfilz75ed7agidiniulic74
*iterative*way. ...*Block*Diagonal (PBD) matrix, is proposed in order to recover*sparse*signals from incomplete linear measurements. ... Acknowledgements This work was partly supported by Grant-in-Aid*for*Scientific Research (B) 21300030, Japan Society*for*the Promotion of Science (JSPS). ...##
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Concurrent Number Cruncher: An Efficient Sparse Linear Solver on the GPU
[chapter]

2007
*
Lecture Notes in Computer Science
*

By combining recent GPU programming techniques with supercomputing strategies (namely

doi:10.1007/978-3-540-75444-2_37
fatcat:icrnxj5jpbh2jmizlloxn64to4
*block*compressed row storage and register*blocking*), we implement a*sparse*generalpurpose linear solver which outperforms ... dense*matrices*(CuBLAS). ... Acknowledgements The authors thank the members of the GOCAD research consortium*for*their support (www.gocad.org), Xavier Cavin, and Bruno Stefanizzi from ATI*for*providing the CTM API and the associated ...
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