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What is the optimal algorithm for computing the eigenvalues/eigenvectors of an arbitrary matrix? What about the singular value decomposition (SVD)? What does optimal even mean in this context? I'll survey some recent efforts to answer these questions, from both a theoretical computer science and classical numerical analysis perspective. I'll also discuss related open research directions; despite the fact that the earliest eigenvalue algorithms date back nearly 200 years, there's still lots to be discovered here!
Data movement is often the dominant cost (in both time and energy) for tensor operations. A long line of work has gone into both reducing this cost and finding bounds on it, largely using geometric and graph-based methods. This talk describes a different approach to this problem using tools from information theory and database theory, and how these techniques can be applied to sparse linear algebra problems.
A welcome event for all new Simons fellows to introduce them to the Simons Institute community. All new fellows will present a 10-minute talk followed by 5 minutes for Q&A with the aim of making introductions to each other, program participants, and the...
Koopman operators recast nonlinear dynamics as infinite-dimensional linear systems, enabling spectral analysis of time-series data—effectively, data-driven infinite-dimensional numerical linear algebra. Over the past decade, they’ve found widespread use in...
One way to obtain spaces of matrices with generically nonmaximal rank comes from choosing "intermediate" maps arising in objects known as minimal free resolutions. This means that resolutions that are equivariant with respect to a large symmetry group will...
Ziyang is a fourth-year PhD candidate at UC Riverside. He is interested in designing efficient parallel algorithms and data structures that have good theoretical and practical benefits. His current research focus is on parallel spatial indexes, e.g., kd...
Aadirupa Saha is an Assistant Professor in the Department of Computer Science at the University of Illinois Chicago (UIC), where she belongs to the UIC CS Theory group, and a member of the IDEAL Institute. Prior to this, she was a Research Scientist at...
Gauri Joshi is an associate professor in the ECE department at Carnegie Mellon University. Gauri completed her Ph.D. from MIT EECS, and received her B.Tech and M.Tech from the Indian Institute of Technology (IIT) Bombay. Her awards include the MIT...
Over the past twenty years, randomized dimensionality reduction, commonly known as sketching, has established itself as a fundamental tool in the theory and practice of matrix computations. This talk will provide an overview of sketching, describing what...