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Edmond Chow
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2020 – today
- 2024
- [j41]Difeng Cai, Hua Huang, Edmond Chow, Yuanzhe Xi:
Data-Driven Construction of Hierarchical Matrices With Nested Bases. SIAM J. Sci. Comput. 46(2): S24-S50 (2024) - [j40]Shifan Zhao, Tianshi Xu, Hua Huang, Edmond Chow, Yuanzhe Xi:
An Adaptive Factorized Nyström Preconditioner for Regularized Kernel Matrices. SIAM J. Sci. Comput. 46(4): 2351- (2024) - [j39]Boqin Zhang, Xin Jing, Qimen Xu, Shashikant Kumar, Abhiraj Sharma, Lucas Erlandson, Sushree Jagriti Sahoo, Edmond Chow, Andrew J. Medford, John E. Pask, Phanish Suryanarayana:
SPARC v2.0.0: Spin-orbit coupling, dispersion interactions, and advanced exchange-correlation functionals. Softw. Impacts 20: 100649 (2024) - [j38]Hua Huang, Edmond Chow:
Exploring the Design Space of Distributed Parallel Sparse Matrix-Multiple Vector Multiplication. IEEE Trans. Parallel Distributed Syst. 35(11): 1977-1988 (2024) - [c40]Mikhail Khodak, Edmond Chow, Maria-Florina Balcan, Ameet Talwalkar:
Learning to Relax: Setting Solver Parameters Across a Sequence of Linear System Instances. ICLR 2024 - [i15]Shifan Zhao, Jiaying Lu, Carl Ji Yang, Edmond Chow, Yuanzhe Xi:
Efficient Two-Stage Gaussian Process Regression Via Automatic Kernel Search and Subsampling. CoRR abs/2405.13785 (2024) - [i14]Difeng Cai, Edmond Chow, Yuanzhe Xi:
Posterior Covariance Structures in Gaussian Processes. CoRR abs/2408.07379 (2024) - 2023
- [j37]Edmond Chow:
Editorial. Int. J. High Perform. Comput. Appl. 37(6): 649 (2023) - [j36]Difeng Cai, Edmond Chow, Yuanzhe Xi:
Data-driven linear complexity low-rank approximation of general kernel matrices: A geometric approach. Numer. Linear Algebra Appl. 30(6) (2023) - [j35]Paritosh Ramanan, Murat Yildirim, Nagi Gebraeel, Edmond Chow:
Differentially Private Decentralized Generator Maintenance and Operations for Power Networks. IEEE Trans. Control. Netw. Syst. 10(2): 972-982 (2023) - [i13]Shifan Zhao, Tianshi Xu, Edmond Chow, Yuanzhe Xi:
An Adaptive Factorized Nyström Preconditioner for Regularized Kernel Matrices. CoRR abs/2304.05460 (2023) - [i12]Mikhail Khodak, Edmond Chow, Maria-Florina Balcan, Ameet Talwalkar:
Learning to Relax: Setting Solver Parameters Across a Sequence of Linear System Instances. CoRR abs/2310.02246 (2023) - 2022
- [j34]Xin Xing, Hua Huang, Edmond Chow:
A hierarchical matrix approach for computing hydrodynamic interactions. J. Comput. Phys. 448: 110761 (2022) - [c39]Yu-Hsiang Mike Tsai, Pratik Nayak, Edmond Chow, Hartwig Anzt:
Implementing Asynchronous Jacobi Iteration on GPUs. ScalAH@SC 2022: 1-9 - [c38]Hua Huang, Edmond Chow:
CA3DMM: A New Algorithm Based on a Unified View of Parallel Matrix Multiplication. SC 2022: 28:1-28:15 - [i11]Difeng Cai, Hua Huang, Edmond Chow, Yuanzhe Xi:
Data-driven Construction of Hierarchical Matrices with Nested Bases. CoRR abs/2206.01885 (2022) - [i10]Difeng Cai, Edmond Chow, Yuanzhe Xi:
Data-Driven Linear Complexity Low-Rank Approximation of General Kernel Matrices: A Geometric Approach. CoRR abs/2212.12674 (2022) - 2021
- [j33]Edmond Chow, Andreas Frommer, Daniel B. Szyld:
Asynchronous Richardson iterations: theory and practice. Numer. Algorithms 87(4): 1635-1651 (2021) - [j32]Xin Xing, Hua Huang, Edmond Chow:
Efficient Construction of an HSS Preconditioner for Symmetric Positive Definite ℋ2 Matrices. SIAM J. Matrix Anal. Appl. 42(2): 683-707 (2021) - [j31]Qimen Xu, Abhiraj Sharma, Benjamin M. Comer, Hua Huang, Edmond Chow, Andrew J. Medford, John E. Pask, Phanish Suryanarayana:
SPARC: Simulation Package for Ab-initio Real-space Calculations. SoftwareX 15: 100709 (2021) - [j30]Hua Huang, Xin Xing, Edmond Chow:
H2Pack: High-performance H2 Matrix Package for Kernel Matrices Using the Proxy Point Method. ACM Trans. Math. Softw. 47(1): 3:1-3:29 (2021) - 2020
- [j29]Xin Xing, Edmond Chow:
Interpolative Decomposition via Proxy Points for Kernel Matrices. SIAM J. Matrix Anal. Appl. 41(1): 221-243 (2020) - [j28]Xin Xing, Edmond Chow:
Fast Coulomb Matrix Construction via Compressing the Interactions Between Continuous Charge Distributions. SIAM J. Sci. Comput. 42(1): A162-A186 (2020) - [j27]Christian Glusa, Erik G. Boman, Edmond Chow, Sivasankaran Rajamanickam, Daniel B. Szyld:
Scalable Asynchronous Domain Decomposition Solvers. SIAM J. Sci. Comput. 42(6): C384-C409 (2020) - [c37]Lucas Erlandson, Difeng Cai, Yuanzhe Xi, Edmond Chow:
Accelerating Parallel Hierarchical Matrix-Vector Products via Data-Driven Sampling. IPDPS 2020: 749-758 - [c36]Florent Lopez, Edmond Chow, Stanimire Tomov, Jack J. Dongarra:
Asynchronous SGD for DNN training on Shared-memory Parallel Architectures. IPDPS Workshops 2020: 995-998 - [c35]Rick Archibald, Edmond Chow, Eduardo F. D'Azevedo, Jack J. Dongarra, Markus Eisenbach, Rocco Febbo, Florent Lopez, Daniel Nichols, Stanimire Tomov, Kwai Wong, Junqi Yin:
Integrating Deep Learning in Domain Sciences at Exascale. SMC 2020: 35-50 - [i9]Karan Sikka, Andrew Silberfarb, John Byrnes, Indranil Sur, Edmond Chow, Ajay Divakaran, Richard Rohwer:
Deep Adaptive Semantic Logic (DASL): Compiling Declarative Knowledge into Deep Neural Networks. CoRR abs/2003.07344 (2020) - [i8]Edmond Chow, Andreas Frommer, Daniel B. Szyld:
Asynchronous Richardson iterations. CoRR abs/2009.02015 (2020) - [i7]Paritosh Ramanan, Murat Yildirim, Nagi Gebraeel, Edmond Chow:
Large-Scale Maintenance and Unit Commitment: A Decentralized Subgradient Approach. CoRR abs/2010.09055 (2020) - [i6]Paritosh Ramanan, Murat Yildirim, Nagi Gebraeel, Edmond Chow:
Decentralized and Secure Generation Maintenance with Differential Privacy. CoRR abs/2010.09099 (2020) - [i5]Xin Xing, Hua Huang, Edmond Chow:
Efficient construction of an HSS preconditioner for symmetric positive definite H2 matrices. CoRR abs/2011.07632 (2020) - [i4]Rick Archibald, Edmond Chow, Eduardo F. D'Azevedo, Jack J. Dongarra, Markus Eisenbach, Rocco Febbo, Florent Lopez, Daniel Nichols, Stanimire Tomov, Kwai Wong, Junqi Yin:
Integrating Deep Learning in Domain Sciences at Exascale. CoRR abs/2011.11188 (2020)
2010 – 2019
- 2019
- [j26]Jordi Wolfson-Pou, Edmond Chow:
Modeling the asynchronous Jacobi method without communication delays. J. Parallel Distributed Comput. 128: 84-98 (2019) - [j25]Ichitaro Yamazaki, Edmond Chow, Aurélien Bouteiller, Jack J. Dongarra:
Performance of asynchronous optimized Schwarz with one-sided communication. Parallel Comput. 86: 66-81 (2019) - [c34]Jordi Wolfson-Pou, Edmond Chow:
Asynchronous Multigrid Methods. IPDPS 2019: 101-110 - [c33]Hartwig Anzt, Tobias Ribizel, Goran Flegar, Edmond Chow, Jack J. Dongarra:
ParILUT - A Parallel Threshold ILU for GPUs. IPDPS 2019: 231-241 - [c32]Hua Huang, Edmond Chow:
Overlapping Communications with Other Communications and Its Application to Distributed Dense Matrix Computations. IPDPS 2019: 501-510 - [i3]Paritosh Ramanan, Murat Yildirim, Edmond Chow, Nagi Gebraeel:
An Asynchronous, Decentralized Solution Framework for the Large Scale Unit Commitment Problem. CoRR abs/1904.03560 (2019) - 2018
- [j24]Edmond Chow, Hartwig Anzt, Jennifer A. Scott, Jack J. Dongarra:
Using Jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning. J. Parallel Distributed Comput. 119: 219-230 (2018) - [j23]Difeng Cai, Edmond Chow, Lucas Erlandson, Yousef Saad, Yuanzhe Xi:
SMASH: Structured matrix approximation by separation and hierarchy. Numer. Linear Algebra Appl. 25(6) (2018) - [j22]Xin Xing, Edmond Chow:
Preserving Positive Definiteness in Hierarchically Semiseparable Matrix Approximations. SIAM J. Matrix Anal. Appl. 39(2): 829-855 (2018) - [j21]Hartwig Anzt, Edmond Chow, Jack J. Dongarra:
ParILUT - A New Parallel Threshold ILU Factorization. SIAM J. Sci. Comput. 40(4): C503-C519 (2018) - [c31]Jordi Wolfson-Pou, Edmond Chow:
Convergence Models and Surprising Results for the Asynchronous Jacobi Method. IPDPS 2018: 940-949 - [c30]Hua Huang, Edmond Chow:
Accelerating quantum chemistry with vectorized and batched integrals. SC 2018: 41:1-41:14 - [i2]Christian A. Glusa, Paritosh Ramanan, Erik G. Boman, Edmond Chow, Sivasankaran Rajamanickam:
Asynchronous One-Level and Two-Level Domain Decomposition Solvers. CoRR abs/1808.08172 (2018) - 2017
- [j20]Goutham Kamath, Lei Shi, Edmond Chow, Wen-Zhan Song:
Distributed tomography with adaptive mesh refinement in sensor networks. Int. J. Sens. Networks 23(1): 40-52 (2017) - [j19]Rachel Levy, Edmond Chow, Byong Kwon, Katherine Socha, Maeve McCarthy, Peter R. Turner:
SIAM Education Subcommittee Report on Undergraduate Degree Programs in Applied Mathematics. SIAM Rev. 59(1): 199-204 (2017) - [c29]Paritosh Ramanan, Murat Yildirim, Edmond Chow, Nagi Gebraeel:
Asynchronous Decentralized Framework for Unit Commitment in Power Systems. ICCS 2017: 665-674 - [c28]Jordi Wolfson-Pou, Edmond Chow:
Distributed southwell: an iterative method with low communication costs. SC 2017: 48 - [c27]Evan Coleman, Masha Sosonkina, Edmond Chow:
Fault tolerant variants of the fine-grained parallel incomplete LU factorization. SpringSim (HPC) 2017: 15:1-15:12 - 2016
- [j18]Edmond Chow, Xing Liu, Sanchit Misra, Marat Dukhan, Mikhail Smelyanskiy, Jeff R. Hammond, Yunfei Du, Xiangke Liao, Pradeep Dubey:
Scaling up Hartree-Fock calculations on Tianhe-2. Int. J. High Perform. Comput. Appl. 30(1): 85-102 (2016) - [j17]Benjamin P. Pritchard, Edmond Chow:
Horizontal vectorization of electron repulsion integrals. J. Comput. Chem. 37(28): 2537-2546 (2016) - [j16]Hartwig Anzt, Edmond Chow, Jens Saak, Jack J. Dongarra:
Updating incomplete factorization preconditioners for model order reduction. Numer. Algorithms 73(3): 611-630 (2016) - [c26]Jordi Wolfson-Pou, Edmond Chow:
Reducing Communication in Distributed Asynchronous Iterative Methods. ICCS 2016: 1906-1916 - [c25]Hartwig Anzt, Edmond Chow, Thomas Huckle, Jack J. Dongarra:
Batched Generation of Incomplete Sparse Approximate Inverses on GPUs. ScalA@SC 2016: 49-56 - [p2]Hartwig Anzt, Edmond Chow, Daniel B. Szyld, Jack J. Dongarra:
Domain Overlap for Iterative Sparse Triangular Solves on GPUs. Software for Exascale Computing 2016: 527-545 - 2015
- [j15]Edmond Chow, Aftab Patel:
Fine-Grained Parallel Incomplete LU Factorization. SIAM J. Sci. Comput. 37(2) (2015) - [c24]Goutham Kamath, Lei Shi, Edmond Chow, Wen-Zhan Song:
Distributed Multigrid Technique for Seismic Tomography in Sensor Networks. BigCom 2015: 297-310 - [c23]Hartwig Anzt, Edmond Chow, Jack J. Dongarra:
Iterative Sparse Triangular Solves for Preconditioning. Euro-Par 2015: 650-661 - [c22]John Murray, Edmond Chow, Christopher Connolly:
Something In The Way We Move: Quantifying patterns of exploration in virtual spaces. FDG 2015 - [c21]Xiangyu Guo, Xing Liu, Peng Xu, Zhihui Du, Edmond Chow:
Efficient Particle-mesh Spreading on GPUs. ICCS 2015: 120-129 - [c20]Edmond Chow, Hartwig Anzt, Jack J. Dongarra:
Asynchronous Iterative Algorithm for Computing Incomplete Factorizations on GPUs. ISC 2015: 1-16 - [c19]Kiran Pamnany, Sanchit Misra, Md. Vasimuddin, Xing Liu, Edmond Chow, Srinivas Aluru:
Dtree: Dynamic Task Scheduling at Petascale. ISC 2015: 122-138 - 2014
- [j14]Edmond Chow, Yousef Saad:
Preconditioned Krylov Subspace Methods for Sampling Multivariate Gaussian Distributions. SIAM J. Sci. Comput. 36(2) (2014) - [c18]Xing Liu, Edmond Chow:
Large-Scale Hydrodynamic Brownian Simulations on Multicore and Manycore Architectures. IPDPS 2014: 563-572 - [c17]Xing Liu, Aftab Patel, Edmond Chow:
A New Scalable Parallel Algorithm for Fock Matrix Construction. IPDPS 2014: 902-914 - [c16]M. Graham Lopez, Mitchel D. Horton, Edmond Chow:
Large-scale Hydrodynamic Brownian Simulations on Multicore and GPU Architectures. XSEDE 2014: 9:1-9:2 - 2013
- [c15]Xing Liu, Mikhail Smelyanskiy, Edmond Chow, Pradeep Dubey:
Efficient sparse matrix-vector multiplication on x86-based many-core processors. ICS 2013: 273-282 - [c14]Daniele Paolo Scarpazza, Douglas J. Ierardi, Adam K. Lerer, Kenneth M. Mackenzie, Albert C. Pan, Joseph A. Bank, Edmond Chow, Ron O. Dror, J. P. Grossman, Daniel Killebrew, Mark A. Moraes, Cristian Predescu, John K. Salmon, David E. Shaw:
Extending the Generality of Molecular Dynamics Simulations on a Special-Purpose Machine. IPDPS 2013: 933-945 - [c13]Ted E. Senator, Henry G. Goldberg, Alex Memory, William T. Young, Brad Rees, Robert Pierce, Daniel Huang, Matthew Reardon, David A. Bader, Edmond Chow, Irfan A. Essa, Joshua Jones, Vinay Bettadapura, Duen Horng Chau, Oded Green, Oguz Kaya, Anita Zakrzewska, Erica Briscoe, Rudolph L. Mappus IV, Robert McColl, Lora Weiss, Thomas G. Dietterich, Alan Fern, Weng-Keen Wong, Shubhomoy Das, Andrew Emmott, Jed Irvine, Jay Yoon Lee, Danai Koutra, Christos Faloutsos, Daniel D. Corkill, Lisa Friedland, Amanda Gentzel, David D. Jensen:
Detecting insider threats in a real corporate database of computer usage activity. KDD 2013: 1393-1401 - 2012
- [j13]Massimiliano Ferronato, Edmond Chow, Kok-Kwang Phoon:
Preconditioning Techniques for Sparse Linear Systems. J. Appl. Math. 2012: 518165:1-518165:3 (2012) - [c12]Zhichen Xia, Chris H. Q. Ding, Edmond Chow:
Robust Kernel Nonnegative Matrix Factorization. ICDM Workshops 2012: 522-529 - [c11]Xing Liu, Edmond Chow, Karthikeyan Vaidyanathan, Mikhail Smelyanskiy:
Improving the Performance of Dynamical Simulations Via Multiple Right-Hand Sides. IPDPS 2012: 36-47 - [c10]William B. March, Kenneth Czechowski, Marat Dukhan, Thomas Benson, Dongryeol Lee, Andrew J. Connolly, Richard W. Vuduc, Edmond Chow, Alexander G. Gray:
Optimizing the computation of n-point correlations on large-scale astronomical data. SC 2012: 74 - 2011
- [j12]Ron O. Dror, J. P. Grossman, Kenneth M. Mackenzie, Brian Towles, Edmond Chow, John K. Salmon, Cliff Young, Joseph A. Bank, Brannon Batson, Martin M. Deneroff, Jeffrey Kuskin, Richard H. Larson, Mark A. Moraes, David E. Shaw:
Overcoming Communication Latency Barriers in Massively Parallel Scientific Computation. IEEE Micro 31(3): 8-19 (2011) - 2010
- [c9]Ron O. Dror, J. P. Grossman, Kenneth M. Mackenzie, Brian Towles, Edmond Chow, John K. Salmon, Cliff Young, Joseph A. Bank, Brannon Batson, Martin M. Deneroff, Jeffrey Kuskin, Richard H. Larson, Mark A. Moraes, David E. Shaw:
Exploiting 162-Nanosecond End-to-End Communication Latency on Anton. SC 2010: 1-12
2000 – 2009
- 2009
- [c8]David E. Shaw, Ron O. Dror, John K. Salmon, J. P. Grossman, Kenneth M. Mackenzie, Joseph A. Bank, Cliff Young, Martin M. Deneroff, Brannon Batson, Kevin J. Bowers, Edmond Chow, Michael P. Eastwood, Doug Ierardi, John L. Klepeis, Jeffrey Kuskin, Richard H. Larson, Kresten Lindorff-Larsen, Paul Maragakis, Mark A. Moraes, Stefano Piana, Yibing Shan, Brian Towles:
Millisecond-scale molecular dynamics simulations on Anton. SC 2009 - [c7]David E. Shaw, Ron O. Dror, John K. Salmon, J. P. Grossman, Kenneth M. Mackenzie, Joseph A. Bank, Cliff Young, Martin M. Deneroff, Brannon Batson, Kevin J. Bowers, Edmond Chow, Michael P. Eastwood, Doug Ierardi, John L. Klepeis, Jeffrey Kuskin, Richard H. Larson, Kresten Lindorff-Larsen, Paul Maragakis, Mark A. Moraes, Stefano Piana, Yibing Shan, Brian Towles:
Millisecond-scale molecular dynamics simulations on Anton. SC 2009 - 2008
- [j11]Bronis R. de Supinski, Martin Schulz, Vasily V. Bulatov, William H. Cabot, Bor Chan, Andrew W. Cook, Erik W. Draeger, James N. Glosli, Jeffrey A. Greenough, Keith W. Henderson, Alison Kubota, Steve Louis, Brian J. Miller, Mehul V. Patel, Thomas E. Spelce, Frederick H. Streitz, Peter L. Williams, Robert K. Yates, Andy Yoo, George Almási, Gyan Bhanot, Alan Gara, John A. Gunnels, Manish Gupta, José E. Moreira, James C. Sexton, Robert Walkup, Charles Archer, François Gygi, Timothy C. Germann, Kai Kadau, Peter S. Lomdahl, Charles A. Rendleman, Michael L. Welcome, William McLendon, Bruce Hendrickson, Franz Franchetti, Stefan Kral, Juergen Lorenz, Christoph W. Überhuber, Edmond Chow, Ümit V. Çatalyürek:
BlueGene/L applications: Parallelism On a Massive Scale. Int. J. High Perform. Comput. Appl. 22(1): 33-51 (2008) - 2006
- [j10]Edmond Chow:
An Aggregation Multilevel Method Using Smooth Error Vectors. SIAM J. Sci. Comput. 27(5): 1727-1741 (2006) - [c6]Kevin J. Bowers, Edmond Chow, Huafeng Xu, Ron O. Dror, Michael P. Eastwood, Brent A. Gregersen, John L. Klepeis, István Kolossváry, Mark A. Moraes, Federico D. Sacerdoti, John K. Salmon, Yibing Shan, David E. Shaw:
Molecular dynamics - Scalable algorithms for molecular dynamics simulations on commodity clusters. SC 2006: 84 - [p1]Edmond Chow, Robert D. Falgout, Jonathan J. Hu, Raymond S. Tuminaro, Ulrike Meier Yang:
A Survey of Parallelization Techniques for Multigrid Solvers. Parallel Processing for Scientific Computing 2006: 179-201 - 2005
- [c5]Marc Barthelemy, Edmond Chow, Tina Eliassi-Rad:
Knowledge Representation Issues in Semantic Graphs for Relationship Detection. AAAI Spring Symposium: AI Technologies for Homeland Security 2005: 91-98 - [c4]Dayne Freitag, Matthias Blume, John Byrnes, Edmond Chow, Sadik Kapadia, Richard Rohwer, Zhiqiang Wang:
New Experiments in Distributional Representations of Synonymy. CoNLL 2005: 25-32 - [c3]Andy Yoo, Edmond Chow, Keith W. Henderson, Will McLendon III, Bruce Hendrickson, Ümit V. Çatalyürek:
A Scalable Distributed Parallel Breadth-First Search Algorithm on BlueGene/L. SC 2005: 25 - [i1]Marc Barthelemy, Edmond Chow, Tina Eliassi-Rad:
Knowledge Representation Issues in Semantic Graphs for Relationship Detection. CoRR abs/cs/0504072 (2005) - 2003
- [j9]Edmond Chow, Panayot S. Vassilevski:
Multilevel block factorizations in generalized hierarchical bases. Numer. Linear Algebra Appl. 10(1-2): 105-127 (2003) - [j8]Edmond Chow:
An unstructured multigrid method based on geometric smoothness. Numer. Linear Algebra Appl. 10(5-6): 401-421 (2003) - [j7]Na Li, Yousef Saad, Edmond Chow:
Crout Versions of ILU for General Sparse Matrices. SIAM J. Sci. Comput. 25(2): 716-728 (2003) - 2001
- [j6]Edmond Chow:
Parallel Implementation and Practical Use of Sparse Approximate Inverse Preconditioners with a Priori Sparsity Patterns. Int. J. High Perform. Comput. Appl. 15(1): 56-74 (2001) - 2000
- [j5]Edmond Chow:
A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners. SIAM J. Sci. Comput. 21(5): 1804-1822 (2000)
1990 – 1999
- 1999
- [c2]Edmond Chow:
A Scalable Parallel Computation of Sparse Approximate Inverse Preconditioners. PP 1999 - 1998
- [j4]Edmond Chow, Yousef Saad:
Approximate Inverse Preconditioners via Sparse-Sparse Iterations. SIAM J. Sci. Comput. 19(3): 995-1023 (1998) - [j3]Tony F. Chan, Edmond Chow, Yousef Saad, Man-Chung Yeung:
Preserving Symmetry in Preconditioned Krylov Subspace Methods. SIAM J. Sci. Comput. 20(2): 568-581 (1998) - [j2]Edmond Chow, Michael A. Heroux:
An Object-Oriented Framework for Block Preconditioning. ACM Trans. Math. Softw. 24(2): 159-183 (1998) - 1997
- [j1]Edmond Chow, Yousef Saad:
Approximate Inverse Techniques for Block-Partitioned Matrices. SIAM J. Sci. Comput. 18(6): 1657-1675 (1997) - [c1]Edmond Chow, Yousef Saad:
Parallel Approximate Inverse Preconditioners. PP 1997