Research

Our research focuses on low-rank tensor approximation and its applications, with emphasis on numerical tensor calculus, nonlinear optimization methods, underlying approximability principles, as well as algebraic and geometric foundations. Some keywords:

• Tensors: geometry of low-rank varieties, tensor networks, higher-order singular values, tensor product operators
• Approximation: functional analytic foundations, approximation rates, singular value estimates, spectral and nuclear norm
• Optimization: block coordinate methods, truncated iterations, Riemannian optimization, rank adaptivity
• Applications: high-dimensional linear equations and eigenvalue problems, signal processing, tensor completion