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Error bounds for the Sherman-Morrison formula and its modification with improved stability
Behnam Hashemi, Yuji Nakatsukasa
It is known that the Sherman--Morrison (SM) formula is not numerically stable. In recent work, we introduced SMIR, an algorithm that incorporates iterative refinement to enhance th…
Instability of the Sherman-Morrison formula and stabilization by iterative refinement
Behnam Hashemi, Yuji Nakatsukasa
Owing to its simplicity and efficiency, the Sherman-Morrison (SM) formula has seen widespread use across various scientific and engineering applications for solving rank-one pertur…
A sequential multilinear Nyström algorithm for streaming low-rank approximation of tensors in Tucker format
Alberto Bucci, Behnam Hashemi
We present a sequential version of the multilinear Nyström algorithm which is suitable for the low-rank Tucker approximation of tensors given in a streaming format. Accessing the t…
RTSMS: Randomized Tucker with single-mode sketching
Behnam Hashemi, Yuji Nakatsukasa
We propose RTSMS (Randomized Tucker via Single-Mode-Sketching), a randomized algorithm for approximately computing a low-rank Tucker decomposition of a given tensor. It uses sketch…