Fast and Cheap Covariance Smoothing
Abstract
We introduce the Tensorized-and-Restricted Krylov (TReK) method, a simple and efficient algorithm for estimating covariance tensors with large observational sizes. TReK extends the Krylov subspace method to incorporate range restrictions, enabling its use in a variety of covariance smoothing applications. By leveraging tensor-matrix operations, it achieves significant improvements in both computational speed and memory cost, improving over existing methods by an order of magnitude. TReK ensures finite-step convergence in the absence of rounding errors and converges fast in practice, making it well-suited for large-scale problems. The algorithm is tensor-free and highly flexible, supporting a wide range of forward and projection tensors.
Fields of Study & Subjects
Tensor decomposition and applications
Matrix Theory and Algorithms
Statistical and numerical algorithms
Publication details
- Journal / source
- Journal of Computational and Graphical Statistics
- Volume
- 35
- Issue
- 3
- Pages
- 1330–1347
- Publication date
- 13 January 2026
- Language
- EN