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- W4300452562 abstract "We introduce a backward stable algorithm for computing the CS decomposition of a partitioned $2n times n$ matrix with orthonormal columns, or a rank-deficient partial isometry. The algorithm computes two $n times n$ polar decompositions (which can be carried out in parallel) followed by an eigendecomposition of a judiciously crafted $n times n$ Hermitian matrix. We prove that the algorithm is backward stable whenever the aforementioned decompositions are computed in a backward stable way. Since the polar decomposition and the symmetric eigendecomposition are highly amenable to parallelization, the algorithm inherits this feature. We illustrate this fact by invoking recently developed algorithms for the polar decomposition and symmetric eigendecomposition that leverage Zolotarev's best rational approximations of the sign function. Numerical examples demonstrate that the resulting algorithm for computing the CS decomposition enjoys excellent numerical stability." @default.
- W4300452562 created "2022-10-03" @default.
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- W4300452562 date "2018-04-24" @default.
- W4300452562 modified "2023-09-27" @default.
- W4300452562 title "A Backward Stable Algorithm for Computing the CS Decomposition via the Polar Decomposition" @default.
- W4300452562 doi "https://doi.org/10.48550/arxiv.1804.09002" @default.
- W4300452562 hasPublicationYear "2018" @default.
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