# On Kosloff Tal-Ezer least-squares quadrature formulas

@article{Cappellazzo2021OnKT, title={On Kosloff Tal-Ezer least-squares quadrature formulas}, author={Giacomo Cappellazzo and Wolfgang Erb and Francesco Marchetti and Davide Poggiali}, journal={ArXiv}, year={2021}, volume={abs/2109.13138} }

In this work, we study a global quadrature scheme for analytic functions on compact intervals based on function values on arbitrary grids of quadrature nodes. In practice it is not always possible to sample functions at optimal nodes with a low-order Lebesgue constant. Therefore, we go beyond classical interpolatory quadrature by lowering the degree of the polynomial approximant and by applying auxiliary mapping functions that map the original quadrature nodes to more suitable fake nodes. More…

## References

SHOWING 1-10 OF 16 REFERENCES

New Quadrature Formulas from Conformal Maps

- Computer Science, MathematicsSIAM J. Numer. Anal.
- 2008

New nonpolynomial quadrature methods are proposed that avoid the usual ellipse of convergence to an infinite strip or another approximately straight-sided domain by conformally mapping the usual circle of convergence.

Quadrature at fake nodes

- 2021

We investigate the use of the so-called mapped bases or fake nodes approach in the framework of numerical integration. We show that such approach is able to mitigate the Gibbs phenomenon when…

ON THE LEBESGUE FUNCTION FOR POLYNOMIAL INTERPOLATION

- Mathematics
- 1978

Properties of the Lebesgue function associated with interpolation at the Chebyshev nodes ${{\{ \cos [(2k - 1)\pi } {(2n)}}],\, k = 1,2, \cdots ,n\} $ are studied. It is proved that the relative…

A Mapped Polynomial Method for High-Accuracy Approximations on Arbitrary Grids

- Mathematics, Computer ScienceSIAM J. Numer. Anal.
- 2016

A new method based on mapped polynomial approximation based on careful selection of the mapping parameter is introduced for the approximation of analytic functions on compact intervals from their pointwise values on arbitrary grids.

A modified Chebyshev pseudospectral method with an O(N –1 ) time step restriction

- Mathematics
- 1989

Abstract The extreme eigenvalues of the Chebyshev pseudospectral differentiation operator are O(N2), where N is the number of grid points. As a result of this, the allowable time step in an explicit…

Multivariate approximation at fake nodes

- Computer ScienceAppl. Math. Comput.
- 2021

This work proposes an effective method for interpolating via mapped bases in the multivariate setting as Fake Nodes Approach (FNA), and the theoretical results are confirmed by various numerical experiments devoted to point out the robustness of the proposed scheme.

Polynomial interpolation via mapped bases without resampling

- Computer Science, MathematicsJ. Comput. Appl. Math.
- 2020

Numerical evidence confirms that such scheme can be applied to mitigate Runge and Gibbs phenomena and is referred to as a new method for univariate polynomial interpolation based on what is called mapped bases.

Treating the Gibbs phenomenon in barycentric rational interpolation via the S-Gibbs algorithm

- Appl. Math. Letters
- 2020

Approximation Theory and Approximation Practice

- 2013

Chebyshev and Fourier Spectral Methods, Dover Publications; Second Edition

- 2013