# A Kogbetliantz-type algorithm for the hyperbolic SVD

@article{Novakovic2020AKA,
title={A Kogbetliantz-type algorithm for the hyperbolic SVD},
author={Vedran Novakovi'c and Sanja Singer},
journal={Numerical Algorithms},
year={2020},
volume={90},
pages={523 - 561}
}
• Published 14 March 2020
• Computer Science
• Numerical Algorithms
In this paper, a two-sided, parallel Kogbetliantz-type algorithm for the hyperbolic singular value decomposition (HSVD) of real and complex square matrices is developed, with a single assumption that the input matrix, of order n, admits such a decomposition into the product of a unitary, a non-negative diagonal, and a J-unitary matrix, where J is a given diagonal matrix of positive and negative signs. When J = ±I, the proposed algorithm computes the ordinary SVD. The paper’s most important…
3 Citations
The vectorized approach is shown to be about three times faster than processing each matrix in isolation, while slightly improving accuracy over the straightforward method for the $2\times 2$ SVD.
The batched EVD is vectorized, with a vector-friendly data layout and the AVX-512 SIMD instructions of Intel CPUs, alongside other key components of a real and a complex OpenMP-parallel Jacobi-type SVD method, inspired by the sequential xGESVJ routines from LAPACK.
The batched EVD is vectorized, with a vector-friendly data layout and the AVX-512 SIMD instructions of Intel CPUs, alongside other key components of a real and a complex OpenMP-parallel Jacobi-type SVD method, inspired by the sequential xGESVJ routines from LAPACK.

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