Erin Claire Carson, Ph.D.
Research Scientist and PRIMUS Fellow 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.
[CV]
[ORCID]
[Google Scholar]
[Github]
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

March 2021: New technical report on mixed precision sstep Lanczos and CG algorithms! You can find MATLAB implementations of these new mixed precision variants on GitHub.

February 2021: I gave the ENLA Seminar talk on Wednesday, February 24 at 16:00 CET. You can find my slides for the talk here, and you can watch the talk on Youtube here!

January 2021: New technical report on the stability of block variants of classical GramSchmidt (with Kathryn Lund and Miroslav Rozložník)!

October 2020: New technical report! A survey of block GramSchmidt algorithms and their numerical stability, complete with a MATLAB package to try them all out (with Kathryn Lund, Miroslav Rozložník, and Stephen Thomas).
All Publications


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, March 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, 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 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. [a href=<"http://www.math.cas.cz/fichier/preprints/IM_20210124200723_43.pdf">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


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.
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 conference on Winter simulation, IEEE Press, 2007, pp. 891899.
[ACMDL]
Teaching

Charles University
 NMNV565: High Performance Computing for Computational Science, Fall/Winter 2020. Instructor.
 NMNV468: Numerical Linear Algebra for Data Science and Informatics. Instructor. Spring/Summer 2020.
 NMNV565: High Performance Computing for Computational Science, Fall/Winter 2019. 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 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.