SHF: Small: From Matrix Computations to Tensor Computations

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Libraries for matrix computations have had a huge impact on computational science since many computations can be cast in terms of linear algebra. As a result, widely used libraries have been available and in broad use for decades. More recently, multi-linear computations, also known as tensor computations, have become important. Application areas include computational chemistry, physics, and large data analysis. Until now, little research has been dedicated towards the development of high quality, high performing libraries for such computations. This project will make strides towards remedying this.This project transfers insights from more than a decade of research and development of dense linear algebra libraries as part of the NSF-sponsored FLAME project to the field of tensor computations. The goal is to create new abstractions for expressing algorithms and their implementations, to derive new algorithms that can take advantage of symmetry in tensors, and discover how to take advantage of the memory hierarchies of modern processors. A prototype library will be implemented and made available to the scientific computing community. Together, this will advance the state-of-the-art in this domain.