5 papers
Monte Carlo Estimators for the Schatten p-norm of Symmetric Positive Semidefinite Matrices
Ethan Dudley, Arvind K. Saibaba, Alen Alexanderian
We present numerical methods for computing the Schatten -norm of positive semi-definite matrices. Our motivation stems from uncertainty quantification and optimal experimental d…
Randomized Algorithms for Generalized Singular Value Decomposition with Application to Sensitivity Analysis
Arvind K. Saibaba, Joseph Hart, Bart van Bloemen Waanders
The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is…
Randomization and reweighted -minimization for A-optimal design of linear inverse problems
Elizabeth Herman, Alen Alexanderian, Arvind K. Saibaba
We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average po…
Randomized algorithms for low-rank tensor decompositions in the Tucker format
Rachel Minster, Arvind K. Saibaba, Misha E. Kilmer
Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored i…
Randomized Discrete Empirical Interpolation Method for Nonlinear Model Reduction
Arvind K. Saibaba
Discrete empirical interpolation method (DEIM) is a popular technique for nonlinear model reduction and it has two main ingredients: an interpolating basis that is computed from a…