  Efficient and accurate low-rank approximation (LRA) methods are of great
significance for large-scale data analysis. Randomized tensor decompositions
have emerged as powerful tools to meet this need, but most existing methods
perform poorly in the presence of noise interference. Inspired by the
remarkable performance of randomized block Krylov iteration (rBKI) in reducing
the effect of tail singular values, this work designs an rBKI-based Tucker
decomposition (rBKI-TK) for accurate approximation, together with a
hierarchical tensor ring decomposition based on rBKI-TK for efficient
compression of large-scale data. Besides, the error bound between the
deterministic LRA and the randomized LRA is studied. Numerical experiences
demonstrate the efficiency, accuracy and scalability of the proposed methods in
both data compression and denoising.
