Introduction

Approximate computing techniques within numerical linear algebra algorithms are raising major interests in the context of exascale-era supercomputers and problems. By approximating all or certain strategic parts of the computation, approximate computing methods can substantially reduce the time, memory, and energy consumption of scientific computing algorithms. In this context, Julia has offered a fantastic playground for the development of approximate computing techniques, such as:

1. Mixed precision: leverage low-precision types like BFloat16, whose hardware support is driven by the needs of Machine Learning, for classical numerical linear algebra.
2. Randomization and sketching: approximate high-dimensional operators (matrices or else) in lower-dimensional spaces, typically by projection, while keeping distances mostly unchanged (oblivious subspace embedding).
3. Low-rank approximations and algorithms: approximate large and dense matrices (or tensors) by lower dimensional factors, like a singular value decomposition (or a tensor train or Tucker decomposition), and algorithms that maintain the low-rank structure throughout.
4. Inexact algorithms: algorithms that make use of controllable errors or approximations in their intermediate computational steps while still achieving the target solution accuracy. For example, inexact Newton's method, inexact Krylov, inexact ADI, etc.

Objective

The main purpose of this minisymposium is to provide a space where people can share and talk about the newest Julia software developments in approximate computing for numerical linear algebra (and beyond). We wish to promote Julia as a tool for driving advancements in approximate computing and highlight the latest exciting Julia packages in this field. Lastly, we would like to end the minisymposium with a panel discussion around the development of an approximate computing ecosystem in Julia.

Target Audience

This call is open to researchers and practitioners describing their use of Julia for studying the numerical behavior or leveraging the computational benefits of approximate computing techniques. Whether you use Julia to validate ideas or to implement a highly performant library/package, or have turned away from Julia after the prototype stage, your insights are very welcome.

Topics of Interest

We encourage submissions that cover a wide range of topics, including but not limited to:

• Adaptive- and mixed-precision algorithms
• Precision emulation
• Randomization and sketching
• Sparse and low-rank approximations

and other techniques of approximate computing, with applications in:

• Control theory
• Optimization
• Machine learning
• Differential equations
• Eigenvalue problems
• Saddle point problems
• Systems of linear equations
• Basic math functions (sin, cos, exp, etc.)

Confirmed Speakers

The minisymposium will include the following confirmed speakers and topics (ordered by first name; exact titles will be finalized later):

• Alexis Montoison (Argonne National Laboratory, USA; to be confirmed): smth related to Krylov.jl
• Andreas Varga (retired, formerly DLR Oberpfaffenhofen, Germany): "MatrixEquations.jl -- a continuous effort to achieve performance and genericity"
• Jonas Schulze (MPI Magdeburg, Germany): "DifferentialRiccatiEquations.jl: solving matrix equations with low-rank solutions"
• Mantas Mikaitis (University of Leeds, UK): "Accuracy of Mathematical Functions in Julia"
• Nicolas Venkovic (TU Munich, Germany): "Locally Subspace-Optimal Iterative Methods in Julia"
• Olivier Cots (IRIT, France): smth related to OptimalControl.jl