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Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis

https://doi.org/10.1002/nla.2364

Saibaba, Arvind K. ; Hart, Joseph ; van Bloemen Waanders, Bart ( February 2021 , Numerical Linear Algebra with Applications)

Abstract
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 challenging. Motivated by applications in hyper‐differential sensitivity analysis (HDSA), we propose new randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization. Detailed error analysis is given which provides insight into the accuracy of the algorithms and the choice of the algorithmic parameters. We demonstrate the performance of our algorithms on test matrices and a large‐scale model problem where HDSA is used to study subsurface flow.

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Structured Matrix Approximations via Tensor Decompositions

https://doi.org/10.1137/21M1418290

Kilmer, Misha E. ; Saibaba, Arvind K. ( December 2022 , SIAM Journal on Matrix Analysis and Applications)

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Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions

https://doi.org/10.1007/s10444-022-09979-7

Saibaba, Arvind K. ; Minster, Rachel ; Kilmer, Misha E. ( October 2022 , Advances in Computational Mathematics)

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Efficient Algorithms for Eigensystem Realization Using Randomized SVD

https://doi.org/10.1137/20M1327616

Minster, Rachel ; Saibaba, Arvind K. ; Kar, Jishnudeep ; Chakrabortty, Aranya ( January 2021 , SIAM Journal on Matrix Analysis and Applications)
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Randomized Discrete Empirical Interpolation Method for Nonlinear Model Reduction

https://doi.org/10.1137/19M1243270

Saibaba, Arvind K. ( January 2020 , SIAM Journal on Scientific Computing)

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Randomized Algorithms for Low-Rank Tensor Decompositions in the Tucker Format

https://doi.org/10.1137/19M1261043

Minster, Rachel ; Saibaba, Arvind K. ; Kilmer, Misha E. ( January 2020 , SIAM Journal on Mathematics of Data Science)

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