Erin Claire Carson

Courant Instructor/Assistant Professor at the Courant Institute of Mathematical Sciences, New York University

My research sits at the intersection of high performance computing, parallel algorithms, scientific computing, and numerical linear algebra.

I received my PhD in Computer Science from U.C. Berkeley in August 2015, advised by James Demmel and Armando Fox.

The course of my life (so far); updated 5/29/17.




Office

619 Warren Weaver Hall
Courant Institute of Mathematical Sciences
New York University
New York, NY 10012

Office 648
60 5th. Ave (Forbes Building)
Center for Data Science
New York University New York, NY 10011

Email: erin.carson@nyu.edu

Fall 2017 Teaching

MATH-UA.0140-003: Linear Algebra. TR 8:55AM-10:45PM. SILV 410.
Office Hours: TBA

Publications

My Google Scholar profile

Matlab implementations for a few of the algorithms in papers below can be found on Github.

PhD Thesis

E. Carson, Communication-Avoiding Krylov Subspace Methods in Theory and Practice, U.C. Berkeley, EECS, 2015. [pdf], [errata]

Manuscripts in Progress

Journal Papers

  • 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. 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

  • "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), Solan, 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


Past Teaching

New York University

  • DS-GA 1004.002: Big Data Lab, 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