The project inEXASCALE aims to change the way people think about designing and analyzing algorithms in the exascale era. On supercomputers that exist today, achieving even close to the peak performance is incredibly difficult if not impossible for many applications.

Techniques designed to improve performance - making computations less expensive by reorganizing an algorithm, making intentional approximations, and using lower precision - all introduce what we can generally call "inexactness". The question is, with all this inexactness involved, does the algorithm still get close enough to the right answer?

The effects of these sources of inexactness have been studied separately, but never together in a holistic way. By studying the combination of different sources of inexactness, we will reveal not only the limitations of these techniques, but also reveal new opportunities for developing algorithms that are both fast and provably accurate.

inEXASCALE

Analyzing and Exploiting Inexactness in Exascale Matrix Computations

PI: Erin Carson
Charles University
Prague, Czech Republic

Publications

Journal Papers
  • P. Vacek, H. Anzt, E. Carson, N. Kohl, U. Ruede, and Y-H. Tsai, Mixed Precision Multigrid with Smoothing Based on Incomplete Cholesky Factorization, SIAM J. Sci. Comput. (accepted; in press), 2026. [preprint]
  • Y. Liu, Y. Ma, and M. Shao, On a Shrink-and-Expand Technique for Symmetric Block Eigensolvers, SIAM J. Sci. Comput. 48(3), pp. A1153-A1183, 2026. [link][preprint]
  • L. Burke, E. Carson and Y. Ma, On the Numerical Stability of Sketched GMRES, SIAM J. Matrix Anal. Appl. 47(3), pp. 1657-1678, 2026. [link][preprint]
  • E. Carson and X. Chen, pychop: Emulating Low-Precision Arithmetic in Numerical Methods and Neural Networks, ACM Trans. Math. Softw. (accepted, in press), 2026. [link][preprint]
  • X. Chen, E. Carson, and C. Kang, LLM-ABBA: Understanding Time Series via Symbolic Approximation, IEEE Trans. Sig. Proc. 74, pp. 1218-1232, 2026. [link][preprint]
  • E. Carson, K. Lund, Y. Ma, and E. Oktay, On the Loss of Orthogonality in Low-Synchronization Variants of Reorthogonalized Block Classical Gram-Schmidt, Lin. Alg. Appl. 732, pp. 162-206, 2026. [link][preprint]
  • J. Martínek, E. Carson, and R. Scheichl, Exploiting Inexact Computations in Multilevel Monte Carlo and Other Sampling Methods, SIAM J. Sci. Comput. 48(2), pp. B141-B164, 2026. [link][preprint]
  • E. Carson and J. Hercík, The Detection and Correction of Silent Errors in Pipelined Krylov Subspace Methods, Numer. Algs. 101, pp. 1175-1210, 2026. [link (open access)][preprint]
  • N. Khan and E. Carson, Mixed Precision Iterative Refinement with Adaptive Precision Sparse Approximate Inverse Preconditioning, Engineering with Computers 41, pp. 3833-3846, 2025. [link (open access)][preprint]
  • E. Carson and I. Daužickaitė, Mixed Precision Sketching for Least-Squares Problems and its Application in GMRES-Based Iterative Refinement, SIAM J. Matrix Anal. Appl. 46(3), pp. 2041-2060, 2025. [link][preprint]
  • E. Carson and I. Daužickaitė, A Comparison of Mixed Precision Iterative Refinement Approaches for Least-Squares Problems, SIAM J. Matrix Anal. Appl. 46(2), pp. 1117-1144, 2025. [link][preprint]
  • E. Carson and Y. Ma, On the Backward Stability of s-step GMRES, SIAM J. Matrix Anal. Appl. 46(3), pp. 2008-2040, 2025. [link][preprint]
  • E. Carson and Y. Ma, A Stable One-Synchronization Variant of Reorthogonalized Block Classical Gram-Schmidt, SIAM J. Sci. Comput. 47(4), pp. A2353-2377, 2025. [link][preprint]
  • E. Carson, X. Chen, and X. Liu, Mixed Precision HODLR Matrices, SIAM J. Sci. Comput. 47(3), pp. A1408-1435, 2025. [link][preprint]
  • E. Carson, K. Lund, Y. Ma, and E. Oktay, Reorthogonalized Pythagorean Variants of Block Classical Gram-Schmidt, SIAM Journal on Matrix Analysis and Applications 46(1), pp. 310-340, 2025. [link][preprint]
  • P. Vacek, E. Carson, and K. M. Soodhalter, The Effect of Approximate Coarsest-Level Solves on the Convergence of Multigrid V-Cycle Methods, SIAM Journal on Scientific Computing 46(4), pp. A2634-A2659, 2024. [link][preprint]
  • E. Carson, J. Liesen, and Z. Strakoš, Towards Understanding CG and GMRES Through Examples, Linear Algebra and its Applications 692, pp. 241-291, 2024. [link]
  • E. Carson and I. Daužickaitė, Single-pass Nyström Approximation in Mixed Precision, SIAM Journal on Matrix Analysis and Applications 45(3), pp. 1361-1391, 2024. [link][preprint]
  • E. Carson and I. Daužickaitė, The Stability of Split-Preconditioned FGMRES in Four Precisions, Electronic Transactions on Numerical Analysis 60, pp. 40-48, 2024. [link]
  • S. Thomas, E. Carson, M. Rozložník, A. Carr, and K. Świrydowicz, Iterated Gauss-Seidel GMRES, SIAM Journal on Scientific Computing 46(2), pp. S254-S279, 2024. [link][preprint]
  • E. Oktay and E. Carson, Mixed Precision Rayleigh Quotient Iteration for Total Least Squares Problems, Numerical Algorithms, 2023. [link][preprint]
  • E. Carson and N. Khan, Mixed Precision Iterative Refinement with Sparse Approximate Inverse Preconditioning, SIAM Journal on Scientific Computing 45(3), pp. C131-C153, 2023. [link][preprint]
Preprints and Technical Reports
  • E. Carson and Y. Ma, Adaptive Accuracy-Driven Splitting in Ozaki Matrix Multiplication and Application to Block LU Factorization, 2026 [preprint]
  • E. Carson, X. Chen, and R. Khan, Integer-Quantized Hierarchical Matrices with Adaptive Bit Allocation, 2026 [preprint]
  • E. Carson, Y. Ma, and M. Shao, A Framework for Trackable and Modular Rounding Error Analysis, 2026 [preprint]
  • E. Agullo et al., Mixed-Precision Computing for Scientific Discovery: Formats, Co-Design, and Responsible Approximation, 2026 [preprint]
  • I. Thanasis and E. Carson, Error Analysis and Precision Selection for Mixed-Precision DEIM-CUR Decompositions, 2026 [preprint]
  • S. Leveque, L. Bergamaschi, Á. Martínez, and E. Carson, Mixed Precision Solvers for the All-at-Once Runge–Kutta Discretization of the Heat Equation, 2026 [preprint]
  • E. Carson and Y. Ma, Asynchronous Jacobi and Randomized Gauss–Seidel Methods in Shared and Distributed Memory: A Unified Convergence-Rate Analysis, 2026 [preprint]
  • E. Carson and X. Chen, Estimating Condition Number with Graph Neural Networks, 2026 [preprint]
  • E. C. Carson, Balancing Inexactness in Mixed Precision Matrix Computations, 2026 [preprint]
  • E. Carson and X. Chen, Precision Autotuning for Linear Solvers via Contextual Bandit-Based RL, 2026 [preprint]
  • R. Khan and E. Carson, Hybrid Hierarchical Matrices with Adaptive Mixed Precision Storage, 2026 [preprint]
  • E. Carson, Y. Ma, and M. Shao, Mixed Precision Thin SVD Algorithms Based on the Gram Matrix, 2026 [preprint]
  • T. Bake, E. Carson, and Y. Ma, Forward and Backward Error Bounds for a Mixed Precision Preconditioned Conjugate Gradient Algorithm, 2025 [preprint]
  • E. Carson, X. Chen, and X. Liu, Computing k-means in Mixed Precision, 2024 [preprint]
  • E. Carson, X. Chen, and C. Kang, Quantized Symbolic Time Series Approximation, 2024 [preprint]

People

PI: Erin C. Carson

Postdocs:

PhD Students:

  • Ioannis Thanasis
  • Thomas Bake Arenas

Graduated PhD Students:

  • Eda Oktay (currently at MPI Magdeburg)
  • Petr Vacek (currently at IFPEN)

Former Postdocs:

Open Positions



No current open positions.
Plain Academic