Development of powerful algorithm for maximal eigenpair

Chen, Mu-Fa; Li, Yue-Shuang

doi:10.1007/s11464-019-0769-5

Cited by 4 publications

(1 citation statement)

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“…We noticed that in many application scenes of eigenvalue computation, for example, in dynamics, it is often necessary to solve only the first few orders of eigenvalues of a large matrix. The desire for the largest eigenvalue is also common in practice [15][16][17]. However, the current QR, MRRR (Multiple Relatively Robust Representations), DC (Divided and Conquer), and Bisection algorithms do not seem to perform sufficient parallel operations if the number of CPU cores (say, 40) is significantly larger than the number of eigenvalues (say, 1) to be solved.…”

Section: Introductionmentioning

confidence: 99%

A Novel Divisional Bisection Method for the Symmetric Tridiagonal Eigenvalue Problem

2022

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The embarrassingly parallel nature of the Bisection Algorithm makes it easy and efficient to program on a parallel computer, but with an expensive time cost when all symmetric tridiagonal eigenvalues are wanted. In addition, few methods can calculate a single eigenvalue in parallel for now, especially in a specific order. This paper solves the issue with a new approach that can parallelize the Bisection iteration. Some pseudocodes and numerical results are presented. It shows our algorithm reduces the time cost by more than 35–70% compared to the Bisection algorithm while maintaining its accuracy and flexibility.

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Section: Introductionmentioning

confidence: 99%