
Batched computation of the singular value decompositions of order two by the AVX512 vectorization
In this paper a vectorized algorithm for simultaneously computing up to ...
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The LAPW method with eigendecomposition based on the Hari–Zimmermann generalized hyperbolic SVD
In this paper we propose an accurate, highly parallel algorithm for the ...
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Fast Eigen Decomposition for LowRank Matrix Approximation
In this paper we present an efficient algorithm to compute the eigen dec...
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The Normalized Singular Value Decomposition of NonSymmetric Matrices Using Givens fast Rotations
In this paper we introduce the algorithm and the fixed point hardware to...
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A New High Performance and Scalable SVD algorithm on Distributed Memory Systems
This paper introduces a high performance implementation of ZoloSVD algo...
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Square rootbased multisource early PSD estimation and recursive RETF update in reverberant environments by means of the orthogonal Procrustes problem
Multichannel shorttime Fourier transform (STFT) domainbased processin...
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An implicit Hari–Zimmermann algorithm for the generalized SVD on the GPUs
A parallel, blocked, onesided Hari–Zimmermann algorithm for the general...
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A Kogbetliantztype algorithm for the hyperbolic SVD
In this paper a twosided, parallel Kogbetliantztype 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 nonnegative diagonal, and a Junitary 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 contribution—a derivation of formulas for the HSVD of 2× 2 matrices—is presented first, followed by the details of their implementation in floatingpoint arithmetic. Next, the effects of the hyperbolic transformations on the columns of the iteration matrix are discussed. These effects then guide a redesign of the dynamic pivot ordering, being already a wellestablished pivot strategy for the ordinary Kogbetliantz algorithm, for the general, n× n HSVD. A heuristic but sound convergence criterion is then proposed, which contributes to high accuracy demonstrated in the numerical testing results. Such a JKogbetliantz algorithm as presented here is intrinsically slow, but is nevertheless usable for matrices of small orders.
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