Implementing a Tiled Singular Value Decomposition: A Framework for Tiled Linear Algebra in Julia

High-performance computing (HPC) is essential for scientific research, enabling complex simulations and analyses across various fields. However, the specialized knowledge required to utilize HPC effectively can be a barrier for many scientists. This work introduces a hardware-agnostic, large-scale tiled linear algebra framework in Julia designed to enhance accessibility and usability without compromising performance. By providing a flexible abstraction layer, the framework simplifies the development and testing of new algorithms across diverse computing architectures. Julia language’s multiple-dispatch and type inference facilitate the development of type-agnostic, hardware-agnostic, and multi-use frameworks by allowing composability. Utilizing a tiled approach, the implemented framework improves data locality, parallelism, and scalability, making it well-suited for modern heterogeneous environments. Its practical benefits are demonstrated through the implementation of tiled QR-based singular value decomposition (SVD), demonstrating how it streamlines the development process and accelerates scientific discovery. The developed framework is used to implement an in-GPU tiled SVD and an out-of-core GPU-accelerated SVD. Furthermore, its extensibility is demonstrated by implementing a tiled QR algorithm. This work aims to democratize HPC resources by bridging the gap between advanced computational capabilities and user accessibility, empowering a broader range of scientists to fully leverage modern computing technologies.

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Center for Computational Science and Engineering

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2024

Author dc:creator

• Ringoot, Evelyne

Advisor dc:contributor.advisor

• Edelman, Alan

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/157092

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/157092