Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight

DOI10.1016/j.jat.2004.06.001zbMath1061.30035OpenAlexW1992143608MaRDI QIDQ1885443

Walter Van Assche, Alexander I. Aptekarev

Publication date: 28 October 2004

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2004.06.001

zbMATH Keywords

Padé approximantsstrong asymptoticsRiemann-Hilbert problems

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Approximation in the complex plane (30E10) Padé approximation (41A21) Boundary value problems in the complex plane (30E25) Asymptotic representations in the complex plane (30E15)

Related Items

Padé approximants for functions with branch points -- strong asymptotics of Nuttall-Stahl polynomials ⋮ Bivariate generalized inverse Newton-thiele type matrix Padé approximation ⋮ Convergent interpolatory quadrature schemes ⋮ Numerical Integration of Highly Oscillating Functions ⋮ Convergent interpolation to Cauchy integrals over analytic arcs ⋮ Riemann boundary-value problem for holomorphic matrices on non-rectifiable curve ⋮ Convergent non complete interpolatory quadrature rules ⋮ Padé approximants to certain elliptic-type functions ⋮ Multipoint Schur algorithm and orthogonal rational functions. I: Convergence properties ⋮ On the Riemann-Hilbert problem with a piecewise constant matrix ⋮ Gaussian integration formulas for logarithmic weights and application to 2-dimensional solid-state lattices ⋮ Asymptotic expansions for polynomials orthogonal with respect to a complex non-constant weight function ⋮ Stability of fractional order systems ⋮ A Riemann-Hilbert boundary value problem in a triangle ⋮ The distribution of the zeros of the Hermite-Padé polynomials for a pair of functions forming a Nikishin system ⋮ The Szegő function on a non-rectifiable arc ⋮ Riemann-Hilbert analysis and uniform convergence of rational interpolants to the exponential function ⋮ A two-dimensional matrix Padé-type approximation in the inner product space ⋮ A scalar Riemann boundary value problem approach to orthogonal polynomials on the circle ⋮ Nuttall's theorem with analytic weights on algebraic S-contours ⋮ Multipoint Padé approximants to complex Cauchy transforms with polar singularities ⋮ On the analytical solution of the linear-fractional Riemann problem ⋮ Orthogonal polynomials for modified Gegenbauer weight and corresponding quadratures ⋮ Riemann-Hilbert problem associated with Angelesco systems ⋮ An asymptotic formula for polynomials orthonormal with respect to a varying weight

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotics of diagonal Hermite-Padé polynomials
• Toeplitz matrix techniques and convergence of complex weight Padé approximants
• The isomonodromy approach to matrix models in 2D quantum gravity
• Weighted approximation with varying weight
• Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
• Padé polynomial asymptotics from a singular integral equation
• Uniform convergence of Padé diagonal approximants for hyperelliptic functions
• ASYMPTOTIC PROPERTIES OF POLYNOMIALS ORTHOGONAL ON A SYSTEM OF CONTOURS, AND PERIODIC MOTIONS OF TODA LATTICES
• EQUILIBRIUM MEASURE AND THE DISTRIBUTION OF ZEROS OF EXTREMAL POLYNOMIALS
• The isomonodromy approach in the theory of two-dimensional quantum gravitation
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
• A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

This page was built for publication: Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight