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arXiv · 2501.08265

Fast and Cheap Krylov-Based Covariance Smoothing

Ho Yun·Victor M. Panaretos
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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 conjugate gradient method to incorporate range restrictions, enabling its use in a variety of covariance smoothing applications. By leveraging matrix-level 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 also highly flexible, supporting a wide range of forward and projection tensors.

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Ho Yun, Victor M. Panaretos. 2025-01-14. Fast and Cheap Krylov-Based Covariance Smoothing. https://arxiv.org/abs/2501.08265

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