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.


Analyzing and Exploiting Inexactness in Exascale Matrix Computations

PI: Erin Carson
Charles University
Prague, Czech Republic


Journal Papers
  • E. Oktay and E. Carson, Mixed Precision Rayleigh Quotient Iteration for Total Least Squares Problems, Numerical Algorithms (accepted; in press), 2023. [preprint]
  • S. Thomas, E. Carson, M. Rozložník, A. Carr, and K. Świrydowicz, Iterated Gauss-Seidel GMRES, SIAM Journal on Scientific Computing, pp. S254-S279, 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]


PI: Erin C. Carson


PhD Students:

  • Petr Vacek
  • Eda Oktay
  • Noaman Khan

Open Positions

Funded PhD positions are available within the framework of the ERC project "Analyzing and Exploiting Inexactness in Exascale Matrix Computations", led by Dr. Erin Carson at the Faculty of Mathematics and Physics at Charles University. Applications are invited from candidates who have strong background in numerical linear algebra, numerical analysis, parallel computing, or computational/data science application domains. The start date is February 2024, by which time the applicants must hold a Master's degree. Successful candidates must formally enroll in the PhD program at Charles University.

Potential PhD topics include, but are not limited to:

  • Development and analysis of mixed precision numerical linear algebra algorithms
  • Parallel algorithms and implementations for new mixed precision algorithms
  • Numerical linear algebra applied to data analysis and machine learning applications
  • Stability and convergence analysis of asynchronous methods
  • Application of new algorithms within a particular computational or data science discipline

Further details about the project can be found at the project website:

Application deadline: October 31, 2023

Interested candidates should submit the following documents to

  • Curriculum Vitae
  • Cover letter explaining motivation and interest to obtain the position of PhD student
  • Brief summary of Master's thesis (including pdf file of Master's thesis if available)
In addition, the candidate should arrange for two letters of recommendation to be sent directly (i.e., not sent by the applicant) to the same e-mail address before the application deadline.

Selected finalists will be invited to officially apply through the university system; official acceptance in the program will be pending an entrance examination (which can be done virtually) and an English examination (which must be in-person but can be waived in many circumstances). For complete details on the admissions procedure, see

Questions regarding the application can be directed to:
Dr. Erin C. Carson
Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University
Sokolovska 83, 18675 Prague

Plain Academic