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Subspace method for multiparameter-eigenvalue problems based on tensor-train representations KU Leuven University of Antwerp
Automatic rational approximation and linearization of nonlinear eigenvalue problems KU Leuven
We present a method for solving nonlinear eigenvalue problems (NEPs) using rational approximation. The method uses the Antoulas–Anderson algorithm (AAA) of Nakatsukasa, Sète and Trefethen to approximate the NEP via a rational eigenvalue problem. A set-valued variant of the AAA algorithm is also presented for building low-degree rational approximations of NEPs with a large number of nonlinear functions. The rational approximation is embedded in ...
Linearizable Eigenvector Nonlinearities KU Leuven
We present a method to linearize, without approximation, a specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the nonlinearities are expressed by scalar functions that are defined by a quotient of linear functions of the eigenvector. The exact linearization relies on an equivalent multiparameter eigenvalue problem (MEP) that contains the exact solutions of the NEPv. Due to the characterization of MEPs in terms of ...
Two‐level preconditioning for Ridge Regression KU Leuven
Solving linear systems is often the computational bottleneck in real‐life problems. Iterative solvers are the only option due to the complexity of direct algorithms or because the system matrix is not explicitly known. Here, we develop a two‐level preconditioner for regularized least squares linear systems involving a feature or data matrix. Variants of this linear system may appear in machine learning applications, such as ridge regression, ...