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
  • E. Carson and J. Hercík, The Detection and Correction of Silent Errors in Pipelined Krylov Subspace Methods, Numer. Algs. (accepted, in press), 2025. [link (open access)][preprint]
  • E. Carson and I. Daužickaitė, A Comparison of Mixed Precision Iterative Refinement Approaches for Least-Squares Problems, SIAM J. Matrix Anal. Appl. (accepted, in press), 2025. [preprint]
  • E. Carson, X. Chen, and X. Liu, Mixed Precision HODLR Matrices, SIAM Journal on Scientific Computing (accepted; in press), 2025. [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. 310-240, 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
  • J. Martínek, E. Carson, and R. Scheichl, Exploiting Inexact Computations in Multilevel Sampling Methods, 2025. [preprint]
  • L. Burke, E. Carson, and Y. Ma, On the Numerical Stability of Sketched GMRES, 2025. [preprint]
  • E. Carson and Y. Ma, A Stable One-Synchronization Variant of Reorthogonalized Block Classical Gram-Schmidt, 2024. [preprint]
  • E. Carson and Y. Ma, On the Backward Stability of s-step GMRES, 2024. [preprint]
  • E. Carson and I. Daužickaitė, Mixed Precision Sketching for Least-Squares Problems and its Application in GMRES-based Iterative Refinement, 2024. [preprint]
  • E. Carson and J. Hercik, The Detection and Correction of Silent Errors in Pipelined Krylov Subspace Methods, 2024. [preprint]
  • E. Carson, X. Chen, and X. Liu, Computing k-means in Mixed Precision, 2024 [preprint]
  • E. Carson and I. Daužickaitė, A Comparison of Mixed Precision Iterative Refinement Approaches for Least-Squares Problems, 2024. [preprint]
  • N. Khan and E. Carson, Mixed Precision Iterative Refinement with Adaptive Precision Sparse Approximate Inverse Preconditioning, 2023. [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