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]


Currently recruiting PhD students.
See details here. Learn more about the associated PRIMUS project.



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


All Publications

PhD Thesis

E. Carson, Communication-Avoiding Krylov Subspace Methods in Theory and Practice, U.C. Berkeley, EECS, 2015. [pdf], [errata]
Advisors: James Demmel and Armando Fox.

Journal Papers

  • E. Carson and Z. Strakoš, On the Cost of Iterative Computations, Philosophical Transactions A, The Royal Society, 2019 (to appear), DOI 10.1098/rsta.2019.0050. (Note: this paper is a follow-on from the invited lecture at the Royal Society in April 2019; see slides and audio below.)
  • E. C. Carson. An Adaptive s-step Conjugate Gradient Algorithm with Dynamic Basis Updating, Applications of Mathematics, 2019 (to appear).
  • 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.A3549-A3580. [link][PDF]
  • E. Carson, The adaptive s-step conjugate gradient method, SIAM J. Matrix Anal. Appl. 39(3), 2018, pp.1318-1338. [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. A817-A847. [link (open access)]
  • E. Carson and N.J. Higham, A New Analysis of Iterative Refinement and its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems, SIAM J. Sci. Comput. 39(6), 2017, pp. A2834-A2856. [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 s-step 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 Communication-Avoiding Conjugate Gradient Method, Electronic Transactions on Numerical Analysis, 43, 2014, pp. 125-141. [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. 1-155. [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.15-25. [link]
  • E. Carson and J. Demmel. A Residual Replacement Strategy for Improving the Maximum Attainable Accuracy of s-Step Krylov Subspace Methods. SIAM J. Matrix Anal. Appl. 35(1), 2014. [link]
  • E. Carson, N. Knight, and J. Demmel. Avoiding Communication in Nonsymmetric Lanczos-based 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. Write-Avoiding Algorithms, In Proceedings of the 30th IEEE International Parallel and Distributed Processing Symposium (IPDPS), 2016, pp.648-658 [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. s-Step 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. C. Carson. An Adaptive s-step 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. Write-Avoiding Algorithms. Technical Report UCB/EECS-2015-163, U.C. Berkeley, June 2015. [pdf]
  • E. Carson. Avoiding Communication in the Lanczos Bidiagonalization Routine and Associated Lease Squares QR Solver. Technical Report UCB/EECS-2015-15, U.C. Berkeley, April 2015. [pdf]
  • E. Carson and J. Demmel. Accuracy of the s-Step Lanczos Method for the Symmetric Eigenproblem. Technical Report UCB/EECS-2014-165, U.C. Berkeley, September 2014. [pdf]
  • E. Carson and J. Demmel. Error Analysis of the s-Step Lanczos Method in Finite Precision. Technical Report UCB/EECS-2014-55, U.C. Berkeley, May 2014. [pdf]
  • E. Carson and J. Demmel. Analysis of the Finite Precision s-step Biconjugate Gradient Method. Technical Report UCB/EECS-2014-18, 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/EECS-2014-8, EECS Dept., U.C. Berkeley, January 2014. [pdf]
  • E. Carson and J. Demmel. A Residual Replacement Strategy for Improving the Maximum Attainable Accuracy of s-step Krylov Subspace Methods. Technical Report UCB/EECS-2012-197, EECS Dept., U.C. Berkeley, September 2012. [pdf]
  • E. Carson, N. Knight, and J. Demmel. Avoiding Communication in Two-sided Krylov Subspace Methods. Technical Report UCB/EECS-2011-93, EECS Dept., U.C. Berkeley, August 2011. [pdf]

Talks and Extended Abstracts

  • Invited Keynote: "Iterative Refinement in Three Precisions", Third Workshop on Power-Aware Computing (PACO19), Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany, November 5, 2019. [a href="ppt/PACO19.pdf">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", High-Performance Computing in Science and Engineering (HPCSE19), Soláň, Czech Republic, May 20, 2019. [pdf]
  • "Iterative Linear Algebra in the Exascale Era", Numerical Algorithms for High-Performance Computational Science, The Royal Society, London, UK, April 9, 2019. [pdf][Audio Recording]
  • "The s-step Conjugate Gradient Method in Finite Precision", SIAM CSE '19, Spokane, Washington, USA. [pdf]
  • "High-Performance 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 GMRES-based Iterative Refinement for the Solution of Sparse, Ill-Conditioned Linear Systems", International Conference on Preconditioning Techniques for Scientific and Industrial Applications (Preconditioning '17), Vancouver, Canada, August 2, 2017. [pdf]
  • "Communication-Avoiding Algorithms: Challenges and New Results", SIAM Annual Meeting 2017, Pittsburgh, Pennsylvania, July 13, 2017. [pptx][Audio Recording]
  • "The Behavior of Synchronization-Reducing Variants of the Conjugate Gradient Method in Finite Precision", Householder Symposium XX, Blacksburg, Virginia, June 19, 2017. [pdf]
  • Plenary Lecture: "High-Performance 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 Large-Scale Krylov Subspace Methods", Applied Mathematics and Scientific Computing Seminar, Temple University, November 16, 2016. [pdf]
  • "Communication-Avoiding Krylov Subspace Methods in Theory and Practice", SIAM PP '16, Paris, France, April 12, 2016. [pdf]
  • "The s-Step Lanczos Method and its Behavior in Finite Precision", SIAM LA '15, Atlanta, GA, October 30, 2015. [pdf]
  • "Communication-Avoiding Krylov Subspace Methods in Theory and Practice", Development of Modern Methods in Linear Algebra Workshop (DMML), Berkeley, CA, October 23, 2015. [pdf]
  • "Efficient Deflation-Based Preconditioning for the Communication-Avoiding Conjugate Gradient Method", SIAM Conference on Computational Science and Engineering, Salt Lake City, Utah, March 14-18, 2015. [ppt]
  • "Communication-Avoiding 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 2-4, 2014. [pdf]
  • "Improving the Maximum Attainable Accuracy of Communication-Avoiding Krylov Subspace Methods", Householder Symposium XIX, Spa, Belgium, June 8-13, 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 18-21, 2014. [abstract][pptx]
  • "Communication-Avoiding Krylov Subspace Methods in Finite Precision", Bay Area Scientific Computing Day, December 11, 2013. [abstract][pptx]
  • E. Carson and J. Demmel. "Efficient Deflation for Communication-Avoiding Krylov Methods" (extended abstract). Numerical Analysis and Scientific Computation with Applications, Calais, France, June 24-26, 2013. [pdf]
  • E. Carson, N. Knight, and J. Demmel. "Improving the Stability of Communication-Avoiding Krylov Subspace Methods", SIAM Conference on Applied Linear Algebra, Valencia, Spain, June 18-22, 2012.
  • E. Carson, N. Knight, and J. Demmel. "Exploiting Low-Rank Structure in Computing Matrix Powers with Applications to Preconditioning", SIAM Conference on Parallel Processing for Scientific Computing, Savannah, Georgia, February 15-17, 2012 [ pdf | pptx ]
  • E. Carson and J. Demmel. "A Residual Replacement Strategy for Improving the Maximum Attainable Accuracy of Communication-Avoiding Krylov Subspace Methods", 9th International Workshop on Accurate Solution of Eigenvalue Problems, Napa Valley, CA, June 4-7, 2012.
  • E. Carson, N. Knight, and J. Demmel. "Hypergraph partitioning for Computing Matrix Powers" (extended abstract), Fifth SIAM Workshop on Comb. Sci. Comput., pages 31-33, Darmstadt, Germany, May 2011. [pdf]
  • "Recent Progress in Communication-Avoiding Krylov Subspace Methods", Bay Area Scientific Computing Day, Palo Alto, California, May 11, 2011.
  • "Recent Work in Communication-Avoiding Krylov Subspace Methods for Solving Linear Systems", Matrix Computations Seminar, Berkeley, California, October 27, 2010.

Math Poetry

Past Projects


Teaching

Charles University

  • NMNV565: High Performance Computing for Computational Science, Fall 2019. Instructor.

New York University

  • DS-GA 1004: Big Data, Spring 2018. Instructor.
  • MATH-UA 140: Linear Algebra, Fall 2017. Instructor.
  • DS-GA 1004: Big Data, Spring 2017. Instructor.
  • MATH-UA 120: Discrete Mathematics, Fall 2016. Instructor.
  • DS-GA 1004: Big Data, Spring 2016. Instructor.
  • MATH-UA 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