It is recognized that numerical multilinear algebra is playing an increasingly important role across the sciences and engineering. High-dimensional modeling has become ubiquitous because of advances in storage technology. Computatationally-oriented researchers no longer have to be shy about the involvement of unimaginably large, tensor-structured data sets. For the nation to maintain its leadership in scientific computing, the NSF needs to review the progession from matrix-based computational thinking to tensor-based computational thinking and design a coordinated program that will effectively support research in this area. We propose to hold a small, invitation-only, two-day workshop comprised of established researchers that will identify the important open problems and opportunities for discovery in computational multilinear algebra. Getting the right mix of talent is crucial and we plan to assemble representatives from key application areas together with experts in large-scale matrix computations, numerical multilinear algebra, high-performance computing, classical numerical linear algebra, and crucial areas within the field of programming languages. Based on the discussions at the workshop, a document of recommendations will be delivered to the NSF one month after the Workshop.
