## 18 Citations

Rigorous uniform approximation of D-finite functions using Chebyshev expansions

- Computer Science, MathematicsMath. Comput.
- 2017

This work considers the application of classical numerical methods based on a new view of a classical numerical method going back to Clenshaw, combined with a functional enclosure method to compute good uniform approximations of D-finite functions together with rigorous error bounds.

Rigorous Polynomial Approximations and Applications

- Computer Science, Mathematics
- 2011

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

- Computer ScienceInt. J. Circuit Theory Appl.
- 2018

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

- Mathematics, Computer ScienceArXiv
- 2014

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

- Computer Science, MathematicsAutom.
- 2016

A survey on Christoffel–Darboux-type identities of Chebyshev polynomials

- Mathematics
- 2013

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

- Computer ScienceAdvances in Intelligent Systems and Computing
- 2019

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

- Engineering
- 2017

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

- EngineeringSensors
- 2018

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

- Computer Science, MathematicsIEEE Transactions on Automatic Control
- 2013

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.

## References

SHOWING 1-10 OF 60 REFERENCES

The minimality properties of chebyshev polynomials and their lacunary series

- Mathematics, Computer ScienceNumerical Algorithms
- 2008

An extended set of (real) results are given for Chebyshev polynomial minimality in suitably weighted Hölder norms on [−1, 1], as well as (L∞ minimax properties, and bestL1 sufficiency requirements based on ChebysHEv interpolation).

Some estimates of the coefficients in the Chebyshev series expansion of a function

- Mathematics
- 1965

This result is not considered to be very satisfactory. In Sections 2 and 3, we shall consider this problem again, using the method of steepest descents to give an asymptotic estimate for an . In the…

The determination of the Chebyshev approximating polynomial for a differentiable function

- Mathematics
- 1959

If f(x) is continuous over any interval, which we may take, without loss of generality, to be the interval — 1 ^ x á 1, there exists a unique polynomial Pn*(x), of given maximum degree n, which is…

Construction of rational and negative powers of a formal series

- Mathematics
- 1971

Some methods are described for the generation of fractional and negative powers of any formal series, such as Poisson series or Chebyshev series. It is shown that, with the use of the three…

Laurent-Padé approximants to four kinds of Chebyshev polynomial expansions. Part I. Maehly type approximants

- MathematicsNumerical Algorithms
- 2008

Padé-Chebyshev approximants are developed not only to first, but also to second, third and fourth kind ChebysheV polynomial series, based throughout on Laurent series representations of the Maehly type.

The evaluation and estimation of the coefficients in the Chebyshev series expansion of a function

- Mathematics
- 1964

Recent investigations have considered the application of Chebyshev series to finding numerical solutions to frequently occurring problems. The quadrature problem has been considered by Clenshaw and…

Inverting Polynomials and Formal Power Series

- MathematicsSIAM J. Comput.
- 1993

It is shown that computing the nth coefficient of the inverse of a general formal power series requires at least ${n / 2}$ nonscalar operations, and that a corresponding lower bound of $s + {{(n + 1)} / {2 - 1}}$ exists.

A Chebyshev polynomial method for line integrals with singularities

- MathematicsAdv. Comput. Math.
- 1999

A Chebyshev polynomial method for the calculation of line integrals along curves with Cauchy principal value or Hadamard finite part singularities, and makes use of a mapping property of the Hadamards finite part operator to calculate the value of the integral.

Algorithm 277: Computation of Chebyshev series coefficients

- MathematicsCACM
- 1966

modification of the classical least squares method is utilized to approximate a solution to the system of nonlinear equations of condition. After every iteration, the statistic E squared is computed…

Expansion of hypergeometric functions in series of other hypergeometric functions

- Mathematics
- 1961

In a previous paper (1) one of us developed an expansion for the con- fluent hypergeometric function in series of Bessel functions. A different expansion of the same kind given by Buchholz (2) was…