Abstract:
Numerical linear algebra has been a cornerstone of scientific
computing in the 20th century, particularly for solving 1D–3D partial
differential equations. Yet, when faced with high-dimensional
problems, traditional linear-algebraic approaches encounter the
curse of dimensionality, prompting a shift toward highly nonlinear
approximations—most notably deep neural networks trained via
non-convex optimization. Based on tensor-networks, I will highlight
how simple linear algebraic operations remain surprisingly
powerful in modern high-dimensional contexts such as artificial
intelligence and many-body physics. These techniques give rise to a
suite of optimization-free algorithms that sidestep the difficulties of
non-convexity with optimal run time.
High-dimensional linear algebra
13.10.2025 15:00 - 16:30
Organiser:
V. Kazeev, R.I. Bot
Location: