{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/157092"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/157092","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Implementing a Tiled Singular Value Decomposition: A Framework for Tiled Linear Algebra in Julia","abstract":"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.","abstract_html":"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. 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