Erin Claire Carson, Ph.D.
Assistant Professor in the Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University
My research sits at the intersection of numerical linear algebra, high performance computing, and parallel algorithms.
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Office

Sokolovská 49/83
Department of Numerical Mathematics
Faculty of Mathematics and Physics
Charles University
186 75, Praha 8
Czech Republic
Email: carson@karlin.mff.cuni.cz
News and Recent Work

December 2022: Our paper on mixed precision sparse approximate inverse preconditioners and their use within GMRESbased iterative refinement has been accepted to SISC (together with Ph.D. student Noaman Khan)! Find the preprint here.

November 2022: I am pleased to announce that I have received an ERC Starting Grant for my project inEXASCALE, which will analyze and exploit inexactness in exascale matrix computations. See the project website here.

September 2022: I have been invited as a plenary speaker at ILAS 2023. See you in Madrid!

May 2022: New preprint on "Singlepass Nyström approximation in mixed precision" (with postdoc Ieva Daužickaitė) is available here.
All Publications


E. Carson and N. Khan, Mixed Precision Iterative Refinement with Sparse Approximate Inverse Preconditioning, SIAM J. Sci. Comput. (accepted; in press), 2023. [preprint]

E. Oktay and E. Carson, Multistage Mixed Precision Iterative Refinement, Numerical Linear Algebra with Applications, e2434, 2022. [link][preprint]

E. Carson, K. Lund, M. Rozložník, and S. Thomas, Block GramSchmidt Algorithms and their Stability Properties, Linear Algebra and its Applications 638, 150195, 2022. [link][preprint]

E. Carson, T. Gergelits, and I. Yamazaki, Mixed Precision sstep Lanczos and Conjugate Gradient Algorithms, Numerical Linear Algebra with Applications 29(3), e2425, 2022. [link]

E. Carson, K. Lund, and M. Rozložník, The Stability of Block Variants of Classical GramSchmidt, SIAM J. Matrix Anal. Appl. 42(3), 13651380, 2021. [link][preprint]

A. Abdelfattah, H. Anzt, E. G. Boman, E. Carson, et al., A Survey of Numerical Methods Utilizing MixedPrecision Arithmetic, The International Journal of High Performance Computing Applications 35(4), 344369, 2021. [link][arXiv preprint]

E. Carson, N. J. Higham, and S. Pranesh. ThreePrecision GMRESBased Iterative Refinement for Least Squares Problems, SIAM J. Sci. Comput. 42(6), A4063A4083, 2020. [link (open access)]

T. Chen and E. C. Carson. Predictandrecompute conjugate gradient variants, SIAM J. Sci. Comput. 42(5), A3084A3108, 2020. [link]

E. C. Carson, An Adaptive sstep Conjugate Gradient Algorithm with Dynamic Basis Updating, Applications of Mathematics 65(2), 123151, 2020. [link]

E. Carson and Z. Strakoš, On the Cost of Iterative Computations, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378(2166), 2020, DOI 10.1098/rsta.2019.0050. [link] (Note: this paper is a followon from the invited lecture at the Royal Society in April 2019; see slides and audio below.)
 E. Carson, M. Rozložník, Z. Strakoš, P. Tichý, and M. Tůma, The numerical stability analysis of pipelined conjugate gradient methods: Historical context and methodology, SIAM J. Sci. Comput. 40(5), 2018, pp.A3549A3580. [link][PDF]
 E. Carson, The adaptive sstep conjugate gradient method, SIAM J. Matrix Anal. Appl. 39(3), 2018, pp.13181338. [link]
 E. Carson and N.J. Higham, Accelerating the solution of linear systems by iterative refinement in three precisions, SIAM J. Sci. Comput. 40(2), 2018, pp. A817A847. [link (open access)]

E. Carson and N.J. Higham, A New Analysis of Iterative Refinement and its Application to Accurate Solution of IllConditioned Sparse Linear Systems, SIAM J. Sci. Comput. 39(6), 2017, pp. A2834A2856. [link (open access)]

E. Solomonik, E. Carson, N. Knight, and J. Demmel, Tradeoffs between Synchronization, Communication, and Computation in Parallel Linear Algebra Computations, ACM Transactions on Parallel Computing (TOPC), 3(1), 2016. [link]
 E. Carson and J. Demmel, Accuracy of the sstep Lanczos Method for the Symmetric Eigenproblem in Finite Precision, SIAM J. Matrix Anal. Appl. 36 (2), 2015. [link]
 E. Carson, N. Knight, and J. Demmel, An Efficient Deflation Technique for the CommunicationAvoiding Conjugate Gradient Method, Electronic Transactions on Numerical Analysis, 43, 2014, pp. 125141. [link]

G. Ballard, E. Carson, J. Demmel, M. Hoemmen, N. Knight, and O.Schwartz, Communication Lower Bounds and Optimal Algorithms for Numerical Linear Algebra, Acta Numerica, 23 (2014), pp. 1155. [link]
 N. Knight, E. Carson and J. Demmel. Exploiting Data Sparsity in Parallel Matrix Powers Computations, in Parallel Processing and Applied Mathematics, R. Wyrzykowski, J. Dongarra, K. Karczewski, and J. Waniewski, eds., Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2014, pp.1525. [link]
 E. Carson and J. Demmel. A Residual Replacement Strategy for Improving the Maximum Attainable Accuracy of sStep Krylov Subspace Methods. SIAM J. Matrix Anal. Appl. 35(1), 2014. [link]
 E. Carson, N. Knight, and J. Demmel. Avoiding Communication in Nonsymmetric Lanczosbased Krylov Subspace Methods. SIAM J. Sci. Comp. 35 (5), 2013. [link]
Conference Papers


E. Carson, B. Kelley, and I. Yamazaki, Mixed Precision sstep Conjugate Gradient with Residual Replacement on GPUs, In Proceedings of the 36th IEEE International Parallel and Distributed Processing Symposium (IPDPS), 2022, pp. 886896 [link].
 E. Carson, J. Demmel, L. Grigori, N. Knight, P. Koanantakool, O. Schwartz, and H.V. Simhadri. WriteAvoiding Algorithms, In Proceedings of the 30th IEEE International Parallel and Distributed Processing Symposium (IPDPS), 2016, pp. 648658 [link].
 E. Solomonik, E. Carson, N. Knight, and J. Demmel. Tradeoffs Between Synchronization, Communication, and Work in Parallel Linear Algebra Computations. In Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 2014. [link]

S. Williams, E. Carson, M. Lijewski, N. Knight, A. Almgren, B. Van Straalen, and J. Demmel. sStep Krylov Subspace Methods as Bottom Solvers for Geometric Multigrid. In Proceedings of the 28th IEEE International Parallel and Distributed Processing Symposium (IPDPS), 2014. [link]
Technical Reports


E. Carson and I. Daužickaitė, Singlepass Nyström approximation in mixed precision, arXiv:2205.13355, May 2022. [pdf]

S. Thomas, E. Carson, M. Rozložník, A. Carr, and K. Świrydowicz, PostModern GMRES, arXiv:2205.07805, May 2022. [pdf]

E. Carson and N. Khan, Mixed Precision Iterative Refinement with Sparse Approximate Inverse Preconditioning, arXiv:2202.10204, February 2022. [pdf]

E. Oktay and E. Carson, Mixed Precision GMRESbased Iterative Refinement with Recycling, arXiv:2201.09827, January 2022. [pdf]

E. Oktay and E. Carson, Multistage Mixed Precision Iterative Refinement, arXiv:2107.06200, July 2021. [pdf]

E. Carson and T. Gergelits, Mixed Precision sstep Lanczos and Conjugate Gradient Algorithms, arXiv:2103.09210, March 2021. [pdf]

E. Carson, K. Lund, and M. Rozložník, The stability of block variants of classical GramSchmidt, Institute of Mathematics, Czech Academy of Sciences, preprint no. 62021. [pdf]

E. Carson, K. Lund, M. Rozložník, and S. Thomas, An Overview of Block GramSchmidt Methods and their Stability Properties, arXiv:2010.12058, October 2020. [pdf]

E. C. Carson. An Adaptive sstep Conjugate Gradient Algorithm with Dynamic Basis Updating. arXiv:1908.04081, August 2019. [pdf]

E. Carson, J. Demmel, L. Grigori, N. Knight, P. Koanantakool, O. Schwartz, and H.V. Simhadri. WriteAvoiding Algorithms. Technical Report UCB/EECS2015163, U.C. Berkeley, June 2015. [pdf]

E. Carson. Avoiding Communication in the Lanczos Bidiagonalization Routine and Associated Lease Squares QR Solver. Technical Report UCB/EECS201515, U.C. Berkeley, April 2015. [pdf]

E. Carson and J. Demmel. Accuracy of the sStep Lanczos Method for the Symmetric Eigenproblem. Technical Report UCB/EECS2014165, U.C. Berkeley, September 2014. [pdf]

E. Carson and J. Demmel. Error Analysis of the sStep Lanczos Method in Finite Precision. Technical Report UCB/EECS201455, U.C. Berkeley, May 2014. [pdf]
 E. Carson and J. Demmel. Analysis of the Finite Precision sstep Biconjugate Gradient Method. Technical Report UCB/EECS201418, EECS Dept., U.C. Berkeley, March 2014. [pdf]
 E. Solomonik, E. Carson, N. Knight, and J. Demmel. Tradeoffs between Synchronization, Communication, and Work in Parallel Linear Algebra Computations. Technical Report UCB/EECS20148, EECS Dept., U.C. Berkeley, January 2014. [pdf]
 E. Carson and J. Demmel. A Residual Replacement Strategy for Improving the Maximum Attainable Accuracy
of sstep Krylov Subspace Methods. Technical Report UCB/EECS2012197, EECS Dept.,
U.C. Berkeley, September 2012. [pdf]
 E. Carson, N. Knight, and J. Demmel. Avoiding Communication in Twosided Krylov Subspace Methods. Technical Report UCB/EECS201193, EECS Dept., U.C. Berkeley, August 2011. [pdf]
Talks and Extended Abstracts


"Improving the Numerical Behavior of CommunicationAvoiding Krylov Subspace Methods", Faculty of Computer Science Seminar, University of Vienna, September 1, 2022. [pdf]

"Recent Progress in Mixed Precision Numerical Linear Algebra", Advances in Numerical Linear Algebra: Celebrating the 60th Birthday of Nick Higham, Manchester, UK, July 68, 2022. [pdf][video]

"Mixed Precision Iterative Refinement", XXI Householder Symposium on Numerical Linear Algebra, Selva di Fasano, IT, June 1217, 2022. [pdf]

"Opportunities for Mixed Precision in Preconditioned Iterative Methods", International Conference on Preconditioning Techniques for Scientific and Industrial Applications (Preconditioning 2022), Chemnitz, DE, June 810, 2022. [pdf]
 "Challenges and Opportunities in Mixed Precision Numerical Linear Algebra", Innovative Computing Laboratory Lunch Seminar, University of Tennesee, USA, May 13, 2022. [pdf]
 "Exploiting Mixed Precision in Numerical Linear Algebra", 47th Annual University of Arkansas Spring Lecture Series: Numerical Linear Algebra: from Scientific Computing to Data Science Applications, University of Arkansas, USA, May 4, 2022. [pdf]
 "The Hazards and Challenges of Low Precision Computation", SIAM Parallel Processing (PP22), online, February 24, 2022. [pdf]
 "High Performance Mixed Precision Numerical Linear Algebra", Numerical Methods and High Performance Computing for Industrial Applications (SimRace), IFP Energies Nouvelles, France, December 3, 2021. [pdf]

"Exploiting Mixed Precision in Numerical Linear Algebra", MATHICSE Seminar Series, EPFL, Switzerland, November 2, 2021. [pdf]

"Exploiting Mixed Precision in Numerical Linear Algebra", Center for Control, Dynamical Systems, and Computation (CCDC) Seminar Series, U.C. Santa Barbara, online, October 29, 2021. [pdf]

"When FloatingPoint Error Matters: the Hazards and Challenges of LowPrecision Computation", SIAM Annual Meeting, online, July 22, 2021. [pdf]

"Mixed Precision sstep Lanczos and Conjugate Gradient Algorithms", Platform for Advanced Scientific Computing (PASC21), online, July 7, 2021. [pdf]

Invited Talk: "The Cost of Iterative Computations at Scale", Irish Numerical Analysis Forum, Dublin, Ireland (online), July 1, 2021. [pdf]

"The Numerical Stability of Block Classical GramSchmidt Variants", SIAM Conference on Applied Linear Algebra, online, May 18, 2021. [pdf]

Invited Talk: "What do we know about block GramSchmidt?", ENLA Seminar, online, February 24, 2021. [pdf][YouTube video]

Invited Talk: "High Performance Mixed Precision Numerical Linear Algebra", Cornell Scientific Computing and Numerics (SCAN) Seminar, online, November 9, 2020. [pdf]

Invited Talk: "High Performance Mixed Precision Numerical Linear Algebra", KU Leuven Numerical Mathematics (NUMA) Seminar, online, October 29, 2020. [pdf]

Invited Keynote: "Accelerating the Solution of Linear Systems via Multiprecision Arithmetic", Advanced Solvers for Modern Architectures, 7th Applied Mathematics Symposium Muenster, Muenster, DE, November 1113, 2019. [pdf]

Invited Keynote: "Iterative Refinement in Three Precisions", Third Workshop on PowerAware Computing (PACO19), Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany, November 5, 2019. [pdf]

"Iterative Refinement in Three Precisions", Parallel Solution Methods for Systems Arising from PDEs, Centre International De Rencontres Mathématiques (CIRM), Luminy, France, September 16, 2019. [pdf]

"The Rise of Multiprecision Computation", Department of Numerical Mathematics Seminar, Charles University, August 20, 2019. [pdf]

"On the Amplification of Rounding Errors", Advances in Numerical Linear Algebra: Celebrating the Centenary of the Birth of James H. Wilkinson, Manchester, UK, May 29, 2019. [pdf][YouTube video]

"The Cost of Iterative Computations", HighPerformance Computing in Science and Engineering (HPCSE19), Soláň, Czech Republic, May 20, 2019. [pdf]

"Iterative Linear Algebra in the Exascale Era", Numerical Algorithms for HighPerformance Computational Science, The Royal Society, London, UK, April 9, 2019. [pdf][Audio Recording]

"The sstep Conjugate Gradient Method in Finite Precision", SIAM CSE '19, Spokane, Washington, USA. [pdf]

"HighPerformance Variants of Krylov Subspace Methods", SNA Winter School 2019, Ostrava, Czech Republic. [Part 1 pdf][Part 2 pdf]

"Exploiting Multiprecision Hardware in Solving Linear Systems and Least Squares Problems", Seminar of Current Problems in Numerical Analysis, Institute of Mathematics, Czech Academy of Sciences, December 14, 2018. [pdf]

"Sparse Matrix Computations in the Exascale Era", Seminar of Numerical Mathematics, Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, November 15, 2018. [pdf]

"Error Bounds for Iterative Refinement in Three Precisions", SIAM AN '18, Portland, Oregon, USA, July 13, 2018. [pdf]

"High Performance Variants of Krylov Subspace Methods", SIAM PP '18, Tokyo, Japan, March 8, 2018. [pdf]

"Preconditioned GMRESbased Iterative Refinement for the Solution of Sparse, IllConditioned Linear Systems", International Conference on Preconditioning Techniques for Scientific and Industrial Applications (Preconditioning '17), Vancouver, Canada, August 2, 2017. [pdf]

"CommunicationAvoiding Algorithms: Challenges and New Results", SIAM Annual Meeting 2017, Pittsburgh, Pennsylvania, July 13, 2017. [pptx][Audio Recording]

"The Behavior of SynchronizationReducing Variants of the Conjugate Gradient Method in Finite Precision", Householder Symposium XX, Blacksburg, Virginia, June 19, 2017. [pdf]

Plenary Lecture: "HighPerformance Krylov Subspace Method Variants and their Behavior in Finite Precision", High Performance Computing in Science and Engineering (HPCSE17), Soláň, Czech Republic, May 24, 2017. [pdf]

"Performance and Stability Tradeoffs in LargeScale Krylov Subspace Methods", Applied Mathematics and Scientific Computing Seminar, Temple University, November 16, 2016. [pdf]

"CommunicationAvoiding Krylov Subspace Methods in Theory and Practice", SIAM PP '16, Paris, France, April 12, 2016. [pdf]

"The sStep Lanczos Method and its Behavior in Finite Precision", SIAM LA '15, Atlanta, GA, October 30, 2015. [pdf]

"CommunicationAvoiding Krylov Subspace Methods in Theory and Practice", Development of Modern Methods in Linear Algebra Workshop (DMML), Berkeley, CA, October 23, 2015. [pdf]

"Efficient DeflationBased Preconditioning for the CommunicationAvoiding Conjugate Gradient Method", SIAM Conference on Computational Science and Engineering, Salt Lake City, Utah, March 1418, 2015. [ppt]

"CommunicationAvoiding Krylov Subspace Methods in Finite Precision", Linear Algebra and Optimization Seminar, ICME, Stanford University, December 4, 2014. [pptx]

"Avoiding Communication in Bottom Solvers for Geometric Multigrid Methods", 8th International Workshop on Parallel Matrix Algorithms and Applications, Lugano, Switzerland, July 24, 2014. [pdf]

"Improving the Maximum Attainable Accuracy of CommunicationAvoiding Krylov Subspace Methods", Householder Symposium XIX, Spa, Belgium, June 813, 2014. [pptx]
 S. Williams, E. Carson, N. Knight, M. Lijewski, A. Almgren, B. van Straalen and J. Demmel. "Avoiding synchronization in geometric multigrid". SIAM Parallel Processing for Scientific Computing, Portland, Oregon, February 1821, 2014. [abstract][pptx]

"CommunicationAvoiding Krylov Subspace Methods in Finite Precision", Bay Area Scientific Computing Day, December 11, 2013. [abstract][pptx]
 E. Carson and J. Demmel. "Efficient Deflation for CommunicationAvoiding Krylov Methods" (extended abstract).
Numerical Analysis and Scientific Computation with Applications, Calais, France, June 2426, 2013. [pdf]
 E. Carson, N. Knight, and J. Demmel. "Improving the Stability of CommunicationAvoiding Krylov Subspace Methods", SIAM Conference on Applied Linear Algebra, Valencia, Spain, June 1822, 2012.
 E. Carson, N. Knight, and J. Demmel. "Exploiting LowRank Structure in Computing Matrix Powers with Applications to Preconditioning", SIAM Conference on Parallel Processing for Scientific Computing, Savannah, Georgia, February 1517, 2012 [ pdf  pptx ]
 E. Carson and J. Demmel. "A Residual Replacement Strategy for Improving the Maximum Attainable Accuracy of CommunicationAvoiding Krylov Subspace Methods", 9th International Workshop on Accurate Solution of Eigenvalue Problems, Napa Valley, CA, June 47, 2012.
 E. Carson, N. Knight, and J. Demmel. "Hypergraph partitioning for Computing Matrix Powers" (extended
abstract), Fifth SIAM Workshop on Comb. Sci. Comput., pages 3133, Darmstadt, Germany, May 2011. [pdf]

"Recent Progress in CommunicationAvoiding Krylov Subspace Methods", Bay Area Scientific Computing Day, Palo Alto, California, May 11, 2011.

"Recent Work in CommunicationAvoiding Krylov Subspace Methods for Solving Linear Systems", Matrix Computations Seminar, Berkeley, California, October 27, 2010.
Teaching

Charles University
 NMNV565: High Performance Computing for Computational Science, Winter 22/23. Instructor.
 NMNV468: Numerical Linear Algebra for Data Science and Informatics, Summer 21/22. Instructor
 NMNV565: High Performance Computing for Computational Science, Winter 21/22. Instructor.
 NMNV565: High Performance Computing for Computational Science, Winter 20/21. Instructor.
 NMNV468: Numerical Linear Algebra for Data Science and Informatics, Summer 19/20. Instructor
 NMNV565: High Performance Computing for Computational Science, Winter 19/20. Instructor.
New York University

DSGA 1004: Big Data, Spring 2018. Instructor.

MATHUA 140: Linear Algebra, Fall 2017. Instructor.

DSGA 1004: Big Data, Spring 2017. Instructor.

MATHUA 120: Discrete Mathematics, Fall 2016. Instructor.

DSGA 1004: Big Data, Spring 2016. Instructor.

MATHUA 120: Discrete Mathematics, Fall 2015. Instructor.
U.C. Berkeley

CS 70: Discrete Mathematics and Probability Theory, Fall 2014. Instructor: Anant Sahai.

Math 54: Linear Algebra and Differential Equations, Spring 2011. Instructor: Constantin Teleman.
University of Virginia

CS 202: Discrete Mathematics, Spring 2009. Instructor: Paul F. Reynolds, Jr.

CS 202: Discrete Mathematics, Fall 2008. Instructor: John C. Knight.

CS 101: Introduction to CS, Fall 2008. Instructor: Tom Horton.
 CS 101: Introduction to CS, Spring 2008 and Fall 2007. Instructor: Kevin Sullivan and Greg Humphreys.
 CS 101x: Introduction to CS (for nonengineers), Fall 2007. Instructor: Jim Cohoon.
Misc

Benchmarks
Math Poetry

[The Lore Ax=b], Dedicated to Jim Demmel on the occasion of his 60th birthday.
Past Projects
 G. Ballard, E. Carson, and N. Knight, Algorithmicbased Fault Tolerance for Matrix Multiplication on Amazon EC2, 2009.
[pdf]
 E. Carson, The Quantification and Management of Uncertainty in Smallpox Intervention Models, Undergraduate Thesis, University of Virginia, 2009.
[pdf]
 J. Carnahan, S. Policastro, E. Carson, P. Reynolds Jr., and R. Kelly, Using Flexible Points in a Developing Simulation of Selective Dissolution in Alloys, in Proceedings of the 39th Winter simulation conference, IEEE Press, 2007, pp. 891899.
[ACMDL]