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Block Iterators for Sparse Matrices

Daniel Langr, Ivan Šimeček, Tomáš Dytrych
2016 Proceedings of the 2016 Federated Conference on Computer Science and Information Systems  
Finding an optimal 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.  ... 
doi:10.15439/2016f35 dblp:conf/fedcsis/LangrSD16 fatcat:s5hc4quiqvhufgjacvcwm26mdu

Iterative Sparse Triangular Solves for Preconditioning [chapter]

Hartwig Anzt, Edmond Chow, Jack Dongarra
2015 Lecture Notes in Computer Science  
We propose using an 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.  ... 
doi:10.1007/978-3-662-48096-0_50 fatcat:k4p5ysqnhza3djruia4kvsc5j4

Scalable task-based algorithm for multiplication of block-rank-sparse matrices

Justus A. Calvin, Cannada A. Lewis, Edward F. Valeev
2015 Proceedings of the 5th Workshop on Irregular Applications Architectures and Algorithms - IA3 '15  
inverse of 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.  ... 
doi:10.1145/2833179.2833186 dblp:conf/sc/CalvinLV15 fatcat:u2cikz45ozgptkp4i7ywlhpnqe

A hardware acceleration technique for gradient descent and conjugate gradient

David Kesler, Biplab Deka, Rakesh Kumar
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 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.  ... 
doi:10.1109/sasp.2011.5941086 dblp:conf/sasp/KeslerDK11 fatcat:o4ahplwirnfoxmvnoiabza2m2a

Conjugate Gradient and Lanczos Methods for Sparse Matrices on Distributed Memory Multiprocessors

A. Basermann
1997 Journal of Parallel and Distributed Computing  
coefficient 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  ... 
doi:10.1006/jpdc.1997.1364 fatcat:zcblw62k4zbebid7az2sgnuh7i

Some results on sparse block factorization iterative methods

Guo Chun-hua
1991 Linear Algebra and its Applications  
We consider the general 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  ... 
doi:10.1016/0024-3795(91)90295-8 fatcat:lkztrgrgrfaqxdikxkvoujbgxq

Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices

Jun Zhang
2000 Applied Numerical Mathematics  
We investigate the use of 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  ... 
doi:10.1016/s0168-9274(99)00047-1 fatcat:b65ckmqv5rcmjixyu7tteyij3q

BLOCK MATRIX PRECONDITIONER METHOD FOR THE ELECTRIC FIELD INTEGRAL EQUATION (EFIE) FORMULATION BASED ON LOOP-STAR BASIS FUNCTIONS

Jae-Hyun Yeom, Huicheol Chin, Hyo-Tae Kim, Kyung-Tae Kim
2013 Electromagnetic Waves  
Moreover, to improve the convergence rate of 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.  ... 
doi:10.2528/pier12092403 fatcat:3qx3r75mybfv5d5mmxi2o4lxvq

Sparse Matrices in Matlab*P: Design and Implementation [chapter]

Viral Shah, John R. Gilbert
2004 Lecture Notes in Computer Science  
Matlab*P can store distributed 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] .  ... 
doi:10.1007/978-3-540-30474-6_20 fatcat:7qd2oi37dvewlo4qfp5fzjx7am

Increasing the Locality of Iterative Methods and Its Application to the Simulation of Semiconductor Devices

J.C. Pichel, D.B. Heras, J.C. Cabaleiro, A.J. García-Loureiro, F.F. Rivera
2009 The international journal of high performance computing applications  
In this paper a technique 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.  ... 
doi:10.1177/1094342009106416 fatcat:ilvouiq345by3ioo4245ircqy4

COMPARISONS OF THE PARALLEL PRECONDITIONERS FOR LARGE NONSYMMETRIC SPARSE LINEAR SYSTEMS ON A PARALLEL COMPUTER

SANGBACK MA
2004 International journal of high speed computing  
The results show that Multi-Color 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.  ... 
doi:10.1142/s0129053304000232 fatcat:d33bmydqhvavdknmkzcmktp5vq

Task-Based Algorithm for Matrix Multiplication: A Step Towards Block-Sparse Tensor Computing [article]

Justus A. Calvin, Edward F. Valeev
2015 arXiv   pre-print
These traits conflict with the irregular structure (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  ... 
arXiv:1504.05046v1 fatcat:nid45r6nmbgctmgcw3t7xfbyt4

Approximate Inverse Techniques for Block-Partitioned Matrices

Edmond Chow, Yousef Saad
1997 SIAM Journal on Scientific Computing  
This paper proposes some preconditioning options when the system matrix is in 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] .  ... 
doi:10.1137/s1064827595281575 fatcat:wdbhfuzvyzb7vgvxhpfgxn7jzu

Cross Low-Dimension Pursuit for Sparse Signal Recovery from Incomplete Measurements Based on Permuted Block Diagonal Matrix

Zaixing HE, Takahiro OGAWA, Miki HASEYAMA
2011 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
of the original signal from them in an 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).  ... 
doi:10.1587/transfun.e94.a.1793 fatcat:pd4gfilz75ed7agidiniulic74

Concurrent Number Cruncher: An Efficient Sparse Linear Solver on the GPU [chapter]

Luc Buatois, Guillaume Caumon, Bruno Lévy
2007 Lecture Notes in Computer Science  
By combining recent GPU programming techniques with supercomputing strategies (namely 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  ... 
doi:10.1007/978-3-540-75444-2_37 fatcat:icrnxj5jpbh2jmizlloxn64to4
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