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

MATHUA.0140003: Linear Algebra. TR 8:55AM10:45PM. 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.
 E. Carson and N.J. Higham, A New Analysis of Iterative Refinement and its Application to Accurate Solution of IllConditioned Sparse Linear Systems, submitted for publication, 2017.
Preprint: Technical Report 2017.12, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, March 2017. [preprint]
 E. Carson, The Adaptive sstep Conjugate Gradient Method, submitted for publication, 2016.
Preprint: arXiv:1701.03989, January 2017. [preprint]
 E. Carson, M. Rozloznik, Z. Strakos, P. Tichy, and M. Tuma, On the numerical stability analysis of pipelined Krylov subspace methods, submitted for publication, 2016.
Preprint: Preprint no. 2016/08, Necas Center for Mathematical Modeling, Czech Republic, November 2016. [preprint]
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 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, 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


Plenary Lecture: "HighPerformance 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 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]
Past Teaching

New York University

DSGA 1004.002: Big Data Lab, 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. Topics: Logic, infinity, and induction; applications include undecidability and stable marriage problem. Modular arithmetic and GCDs; applications include primality testing and cryptography. Polynomials; examples include error correcting codes and interpolation. Probability including sample spaces, independence, random variables, law of large numbers; examples include load balancing, existence arguments, Bayesian inference.
 Math 54: Linear Algebra and Differential Equations, Spring 2011. Instructor: Constantin Teleman. Topics: Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; firstorder differential equations with constant coefficients. Fourier series and partial differential equations.
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.