On sequences of rational interpolants of the exponential function with unbounded interpolation points

@article{Claeys2011OnSO,
  title={On sequences of rational interpolants of the exponential function with unbounded interpolation points},
  author={Tom Claeys and Franck Wielonsky},
  journal={J. Approx. Theory},
  year={2011},
  volume={171},
  pages={1-32}
}

Figures from this paper

Riemann-Hilbert Characterisation of Rational Functions with a General Distribution of Poles on the Extended Real Line Orthogonal with Respect to Varying Exponential Weights: Multi-Point Pad\'e Approximants and Asymptotics

Given $K$ arbitrary poles, which are neither necessarily distinct nor bounded, on the extended real line, a corresponding ordered base of rational functions orthogonal with respect to varying

On Uniform Convergence of Diagonal Multipoint Padé Approximants for Entire Functions

We prove that for most entire functions f in the sense of category, a strong form of the Baker–Gammel–Wills conjecture holds. More precisely, there is an infinite sequence $${\mathcal {S}}$$S of

On Uniform Convergence of Diagonal Multipoint Padé Approximants for Entire Functions

  • D. Lubinsky
  • Materials Science
    Constructive Approximation
  • 2017
We prove that for most entire functions f in the sense of category, a strong form of the Baker–Gammel–Wills conjecture holds. More precisely, there is an infinite sequence

The Spurious Side of Diagonal Multipoint Padé Approximants

  • D. Lubinsky
  • Physics
    Topics in Classical and Modern Analysis
  • 2019
We survey at an introductory level, the topic of multipoint Pade approximants, especially the issues of spurious poles and convergence for diagonal rational approximants.

References

SHOWING 1-10 OF 24 REFERENCES

Riemann-Hilbert analysis and uniform convergence of rational interpolants to the exponential function

Rational Interpolation of the Exponential Function

Abstract Let m, n be nonnegative integers and B (m+n) be a set of m + n + 1 real interpolation points (not necessarily distinct). Let Rm,n = P m,n/Qm.n be the unique rational function with deg Pm,n ≤

Rational Approximation to the Exponential Function with Complex Conjugate Interpolation Points

Different convergence results and precise estimates for the error function in compact sets of C that generalize the classical properties of Pade approximants to the exponential function are obtained.

Orthogonal polynomials with complex-valued weight function, II

AbstractIn this paper we continue our study of the asymptotic behavior of polynomialsQmn(z), m, n ∈N, of degree≤n satisfying the orthogonal relation(*) $$( * )\oint_c {\zeta ^l Q_{mn} (\zeta )}

Quadratic Hermite-Padé polynomials associated with the exponential function

  • H. Stahl
  • Mathematics
    J. Approx. Theory
  • 2003

Orthogonal polynomials with complex-valued weight function, I

AbstractIn this paper we investigate the asymptotic behavior of polynomialsQmn(z), m, n ∈ N, of degree ≤n that satisfy the orthogonal relation $$\oint_c {\zeta ^l Q_{mn} (\zeta )} \frac{{f(\zeta

Zero and pole distribution of diagonal padÉ approximants to the exponential function

Abstract The polynomials Pn and Qm , having degrees n and m respectively, with Pn monic, that solve the approximation problem will be investigated for their asymptotic behaviour, in particular in

UNIFORM ASYMPTOTICS FOR POLYNOMIALS ORTHOGONAL WITH RESPECT TO VARYING EXPONENTIAL WEIGHTS AND APPLICATIONS TO UNIVERSALITY QUESTIONS IN RANDOM MATRIX THEORY

We consider asymptotics for orthogonal polynomials with respect to varying exponential weights wn(x)dx = e−nV(x)dx on the line as n ∞. The potentials V are assumed to be real analytic, with

Rational Interpolation to $e^x $, II

The following estimate is derived for the error in approximating $e^x $ by rational functions. Let $\pi _n $ denote the polynomials of degree at most n.THEOREM. Let$\gamma _1 ,\gamma _2 , \cdots

Quadratic Hermite–Padé Approximation to the Exponential Function: A Riemann–Hilbert Approach

Abstract We investigate the asymptotic behavior of the polynomials p, q, r of degrees n in type I Hermite–Padé approximation to the exponential function, defined by p(z)e-z + q(z) + r(z) ez =