A note on orthogonal polynomials described by Chebyshev polynomials

Castillo, K.; Jesus, M. N. de; Petronilho, J.

doi:10.1016/j.jmaa.2020.124906

Cited by 3 publications

(2 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, a response function approximation method based on Chebyshev orthogonal polynomial [7] piecewise fitting [9][10] is proposed. By appropriately increasing the polynomial degree, overlap rate and the number of piecewise interval segments, the high-level noise can be effectively suppressed, which has strong anti-noise performance.…”

Section: Introductionmentioning

confidence: 99%

High-level noise load identification based on Chebyshev polynomial piecewise fitting

Cui,

Gao

2024

International Conference on Mechatronic Engineering and Artificial Intelligence (MEAI 2023)

View full text Add to dashboard Cite

When the telemetry data noise level is high, the traditional integral moving average processing model has a general effect on noise reduction. In order to improve the noise reduction ability and obtain higher load identification accuracy, a new noise reduction model is constructed based on the Chebyshev orthogonal polynomial and the idea of piecewise overlap. The impact load is simulated by half sine wave. Under the condition of 15 % noise, the error values of load identification results are 1.94 % and 0.76 % respectively after the treatment of integral sliding noise reduction model and Chebyshev noise reduction model. In contrast, the new Chebyshev noise reduction model under high-level noise conditions has better accuracy and wider application.

show abstract

Section: Introductionmentioning

confidence: 99%

High-level noise load identification based on Chebyshev polynomial piecewise fitting

Cui,

Gao

2024

International Conference on Mechatronic Engineering and Artificial Intelligence (MEAI 2023)

View full text Add to dashboard Cite

show abstract

“…The spectral method is different from other numerical calculation methods, mainly in the selection of a class of globally smooth function clusters as trial functions and test functions. Commonly used function clusters include Chebyshev polynomials [22], Legendre polynomials [23], and Fourier functions [24]. The test function clusters are mainly divided into Galerkin, Tau and collocation types.…”

Section: Introductionmentioning

confidence: 99%

A Spectral Method for Two-Dimensional Ocean Acoustic Propagation

Wang

Zhu

et al. 2021

JMSE

View full text Add to dashboard Cite

The accurate calculation of the sound field is one of the most concerning issues in hydroacoustics. The one-dimensional spectral method has been used to correctly solve simplified underwater acoustic propagation models, but it is difficult to solve actual ocean acoustic fields using this model due to its application conditions and approximation error. Therefore, it is necessary to develop a direct solution method for the two-dimensional Helmholtz equation of ocean acoustic propagation without using simplified models. Here, two commonly used spectral methods, Chebyshev–Galerkin and Chebyshev–collocation, are used to correctly solve the two-dimensional Helmholtz model equation. Since Chebyshev–collocation does not require harsh boundary conditions for the equation, it is then used to solve ocean acoustic propagation. The numerical calculation results are compared with analytical solutions to verify the correctness of the method. Compared with the mature Kraken program, the Chebyshev–collocation method exhibits higher numerical calculation accuracy. Therefore, the Chebyshev–collocation method can be used to directly solve the representative two-dimensional ocean acoustic propagation equation. Because there are no model constraints, the Chebyshev–collocation method has a wide range of applications and provides results with high accuracy, which is of great significance in the calculation of realistic ocean sound fields.

show abstract

On the characterizations of third-degree semiclassical forms via polynomial mappings

Marcellán

Khalfallah

2022

Integral Transforms and Special Functions

View full text Add to dashboard Cite

A note on orthogonal polynomials described by Chebyshev polynomials

Cited by 3 publications

References 10 publications

High-level noise load identification based on Chebyshev polynomial piecewise fitting

High-level noise load identification based on Chebyshev polynomial piecewise fitting

A Spectral Method for Two-Dimensional Ocean Acoustic Propagation

On the characterizations of third-degree semiclassical forms via polynomial mappings

Contact Info

Product

Resources

About