Numerical Linear Algebra Group

This minisymposium, organized by Massimiliano Fasi and Mantas Mikaitis with Xiaobo Liu as chair, took place during the 10th International Congress on Industrial and Applied Mathematics which was held on 20-25 August, 2023 at Waseda University, Tokyo, Japan. Here we provide slides of the talks that were delivered during this minisymposium.

Abstract: The comeback that stochastic rounding has made in the last few years can be attributed to the availability of hardware implementing low-precision floating-point arithmetic, as well as to the recognition that, in some applications, this rounding mode can control the growth of rounding errors better than commonly used alternatives. Research has focused not only on obtaining efficient hardware and software implementations, but also on understanding the numerical properties of algorithms that replace round-to-nearest with stochastic rounding. In this minisymposium, we will have an opportunity to learn about recent advances in both directions.

Link to the abstracts of the talks: https://iciam2023.org/registered_data?id=00827#03817.

Implementation of Stochastic Rounding. Mantas Mikaitis, University of Leeds.

This talk is based on

• Stochastic rounding: implementation, error analysis and applications. M. Croci, M. Fasi, N. J. Higham, T. Mary, and M. Mikaitis. R. Soc. Open Sci. 9:3, 2022;
• Stochastic Rounding: Algorithms and Hardware Accelerator by M. Mikaitis. 2021 Int. Joint Conf. Neural Networks (IJCNN). 2021.
• Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations. M. Hopkins, M. Mikaitis, D. Lester, and S. Furber. Phil. Trans. R. Soc. A. 378:2166. 2020.

Software Simulation of Stochastic Rounding. Massimiliano Fasi, Durham University; Mantas Mikaitis, University of Leeds.

This talk is based on

• CPFloat: A C Library for Simulating Low-precision Arithmetic. M. Fasi, M. Mikaitis. ACM Trans. Math. Software. 49:2. 2023.

Bounds on Non-linear Errors for Variance Computation with Stochastic Rounding. El-Mehdi El Arar, Paris-Saclay University-UVSQ- LI-PaRAD; Devan Sohier, Paris-Saclay University-UVSQ- LI-PaRAD; Pablo de Oliveira Castro, Paris-Saclay University-UVSQ- LI-PaRAD; Eric Petit, Intel Corp.

This talk is based on

• Bounds on Non-Linear Errors for Variance Computation with Stochastic Rounding. E M El Arar, D Sohier, P de Oliveira Castro, E Petit. arXiv:2304.05177 [math.NA]. 2023.

Trace estimation via asynchronous stochastic rounding. Lior Horesh, IBM T. J. Watson Research Center; Vasileios Kalantzis, IBM T. J. Watson Research Center; Georgios Kollias, IBM T. J. Watson Research Center; Shashanka Ubaru, IBM T. J. Watson Research Center; Chai Wah Wu, IBM T. J. Watson Research Center.

Update (18/10/2023): The authors have provided the following updated slides, which contain corrections to some of the formulas.