Chebyshev series expansion of inverse polynomials

@article{Mathar2006ChebyshevSE,
  title={Chebyshev series expansion of inverse polynomials},
  author={Richard J. Mathar},
  journal={Journal of Computational and Applied Mathematics},
  year={2006},
  volume={196},
  pages={596-607}
}
  • R. Mathar
  • Published 22 March 2004
  • Mathematics
  • Journal of Computational and Applied Mathematics
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18 Citations
Highly Influential Citations
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5
Methods Citations
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18 Citations

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Citation Type

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Rigorous Polynomial Approximations and Applications
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Several applications are presented: one from standard functions implementation in mathematical libraries (libm), another regarding the computation of Chebyshev series expansions solutions of linear ODEs with polynomial coefficients, and an automatic process for function evaluation with guaranteed accuracy in reconfigurable hardware.
Differential equation description and Chebyshev approximation of linear time‐invariant circuits
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An example of an analogue filter verifies the effectiveness and accuracy of the proposed approximation algorithm and elaborates on the selection process of the order number and the time step length of the Chebyshev expansion according to the demanded truncation error.
Sparse approximate inverses of Gramians and impulse response matrices of large-scale interconnected systems
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The proposed approximation methodology is computationally feasible for interconnected systems with an extremely large number of local subsystems and opens the door to the development of novel methods for distributed estimation, identification and control of large-scale interconnected systems.
Sparse solution of the Lyapunov equation for large-scale interconnected systems
A survey on Christoffel–Darboux-type identities of Chebyshev polynomials
In this paper, we construct some new Christoffel–Darboux-type identities for Chebyshev polynomials of four kinds. We obtain these types of identities for the derivatives of Chebyshev polynomials.
3D Objects Indexing Using Chebyshev Polynomial
TLDR
A numeric calculation of the coefficients of Chebyshev polynomial with maximum precision is proposed for the search of similar 3D objects to a request object model and to minimize the processing time in the large database.
Distributed dynamic load identification based on shape function method and polynomial selection technique
Abstract A new approach based on shape function method of moving least square fitting (SFM_MLSF) and polynomial selection technique is proposed in this paper for distributed dynamic load…
Nonlinear Blind Compensation for Array Signal Processing Application
TLDR
A novel nonlinear blind compensation algorithm aims at the nonlinearity mitigation of array receiver and its spurious-free dynamic range (SFDR) improvement, which will be more precise to estimate the parameters of target signals such as their two-dimensional directions of arrival (2-D DOAs).
Moving Horizon Estimation for Large-Scale Interconnected Systems
TLDR
A novel, distributed MHE method that estimates the state of a local subsystem using only local input-output data is developed by approximating a solution of the MHE problem using the Chebyshev approximation method.
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