ON TENSOR PRODUCT DECOMPOSITION OF $k$-TRIDIAGONAL TOEPLITZ MATRICES

Ohashi, Asuka; Usuda, Tsuyoshi Sasaki; Sogabe, Tomohiro; i}lmaz, F. Y{

doi:10.12732/ijpam.v103i3.14

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…A recent direction in numerical computation research pertains to k-tridiagonal matrices [21][22][23][24][25][26][27][28][29], for which, important algorithms, such as block-diagonalization [21], matrix inverse [22,23,26] and singular value decomposition [30], are improved by several orders of magnitude. A k-tridiagonal matrix [22] T ∈ R n×n is a matrix whose elements lay only on its main and kth upper and lower diagonals, i.e., there are some d ∈ R n and a, b ∈ R n−k , such that…”

Section: Introductionmentioning

confidence: 99%

Scalability of k-Tridiagonal Matrix Singular Value Decomposition

et al. 2021

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Singular value decomposition has recently seen a great theoretical improvement for k-tridiagonal matrices, obtaining a considerable speed up over all previous implementations, but at the cost of not ordering the singular values. We provide here a refinement of this method, proving that reordering singular values does not affect performance. We complement our refinement with a scalability study on a real physical cluster setup, offering surprising results. Thus, this method provides a major step up over standard industry implementations.

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Section: Introductionmentioning

confidence: 99%

Scalability of k-Tridiagonal Matrix Singular Value Decomposition

et al. 2021

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“…Another recent interesting application of the tridiagonal matrices can be found for example in [9,10]. In this paper we turn our attention to the relation of permanents of special tridiagonal matrices with Fibonacci numbers.…”

Section: Introductionmentioning

confidence: 99%