Abstract:
Approximating the trace of matrix functions is an important linear algebraic task, with applications in a diverse collection of fields including quantum physics, computational biology, machine learning, and high performance computing. The most widely used algorithms for this task combine Krylov subspace methods with randomized trace estimators. We survey classic algorithms, and describe several new insights concerning the analysis and implementation of such algorithms. We then discuss the incorporation of new variance reduction techniques for standard trace estimation into such algorithms. Finally, we introduce new algorithms for computing the partial traces of matrix functions, which naturally arise in quantum thermodynamics.
Biography:
Tyler Chen is an Assistant Professor/ Courant Instructor at NYU. His research is centered on the design and analysis of (randomized) Krylov subspace methods, with a particular emphasis on applications relating to matrix functions. Dr. Chen received his PhD in Applied Mathematics from the University of Washington.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai