Abstract

Manal Helal
Future Directions in Tensor-Based Computation and Modeling
High-dimensional modeling is becoming ubiquitous across the sciences and engineering because of advances in sensor technology and storage technology. Computationally-oriented researchers no longer have to avoid what were once intractably large, tensor-structured data sets. The current NSF promotion of “computational thinking” is timely: we need a focused international effort to oversee the transition from matrix-based to tensor-based computational thinking. The successful problem-solving tools provided by the numerical linear algebra com- munity need to be broadened and generalized. However, tensor-based research is not just matrix-based research with additional subscripts. Tensors are data objects in their own right and there is much to learn about their geometry and their connections to statistics and operator theory. This requires full participation of researchers from engineering, the natural sciences, and the information sciences, together with statisticians, mathematicians, numerical analysts, and software/language designers. Representatives from these disciplines participated in the Workshop. We believe that the NSF can help ensure the vitality of “big N” engineering and science by systematically supporting research in tensor-based computation and modeling.