TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.7.2.034
TI  - Matrix method and the suppression of Runge's phenomenon
PY  - 2024/06/05
UR  - https://scipost.org/SciPostPhysCore.7.2.034
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 7
IS  - 2
SP  - 034
A1  - Shen, Shuifa
AU  - Qian, Weiliang
AU  - Zhang, Jie
AU  - Pan, Yu
AU  - Yan, Yupeng
AU  - Shao, Chenggang
AB  - Higher-degree polynomial interpolations carried out on uniformly distributed nodes are often plagued by overfitting, known as Runge's phenomenon. This work investigates Runge's phenomenon and its suppression in various versions of the matrix method for black hole quasinormal modes. It is shown that an appropriate choice of boundary conditions gives rise to desirable suppression of oscillations associated with the increasing Lebesgue constant. For the case of discontinuous effective potentials, where the application of the above boundary condition is not feasible, the recently proposed scheme with delimited expansion domain also leads to satisfactory results. The onset of Runge's phenomenon and its effective suppression are demonstrated by evaluating the relevant waveforms. Furthermore, we argue that both scenarios are either closely related to or practical imitations of the Chebyshev grid. The implications of the present study are also addressed.
ER  -

@Article{10.21468/SciPostPhysCore.7.2.034,
	title={{Matrix method and the suppression of Runge's phenomenon}},
	author={Shui-Fa Shen and Wei-Liang Qian and Jie Zhang and Yu Pan and Yu-Peng Yan and Cheng-Gang Shao},
	journal={SciPost Phys. Core},
	volume={7},
	pages={034},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.7.2.034},
	url={https://scipost.org/10.21468/SciPostPhysCore.7.2.034},
}