A fast singular value decomposition algorithm of general k-tridiagonal matrices

Scalability of k-Tridiagonal Matrix Singular Value Decomposition

“…In this section, we make a modification to the SVD algorithm of [30] to obtain the sorted list of singular values.…”

“…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…”

“…While a recent paper [30] studied complexity, in this paper, we make a thorough experimental study of the applicability and benefit of the SVD algorithm for k-tridiagonal matrices on a grid system and investigate their true scalability. Moreover, we improve on the algorithm of [30] by also sorting the singular values of S, and confirm that this additional post-processing does not alter the scaling potential.…”

“…While a recent paper [30] studied complexity, in this paper, we make a thorough experimental study of the applicability and benefit of the SVD algorithm for k-tridiagonal matrices on a grid system and investigate their true scalability. Moreover, we improve on the algorithm of [30] by also sorting the singular values of S, and confirm that this additional post-processing does not alter the scaling potential. In the previous published results, the new optimized algorithm for SVD of the k-tridiagonal matrix is presented, whereas the current paper focuses on parallelization and performance evaluation in terms of scalability.…”

Determinan Suatu Matriks Toeplitz K-Tridiagonal Menggunakan Metode Reduksi Baris Dan Ekspansi Kofaktor

“…Lebih lanjut, Borowska dan Lacinska [4] juga telah melakukan kajian terkait hubungan nilai eigen matriks toeplitz 2-tridiagonal dengan matriks toeplitz tridiagonal. Penelitian-penelitian terbaru yang secara khusus membahas tentang matriks Toeplitz k-Tridiagonal dapat ditemukan pada [5]- [8]. Beberapa pembahasan ini secara spesifik belum ada yang membahas tentang determinan matriks ktridiagonal.…”