Low precision incomplete Cholesky factorization preconditioning

• Date: 27. 2. 2025
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K1
• Speaker: Miroslav Tůma

The talk will discuss a recent interest in computing approximate matrix factorizations in low precision and employing them as preconditioners within a mixed precision iterative refinement-based approach for solving linear systems of equations. For large sparse systems, incomplete factorization preconditioners can be an attractive option as they are general-purpose and have been successfully applied to solve systems arising from diverse application areas. Our focus is on computing such preconditioners for solving large sparse systems of linear algebraic equations. For simplicity, we are interested in preconditioning systems Ax=b with A symmetric positive definite. Numerical results obtained with the NAG Fortran compiler that correctly simulates the half precision arithmetic illustrate the potential effectiveness of the half precision preconditioner in solving highly ill-conditioned systems to double precision accuracy.