Orthogonal polynomials in \(L^ 1\)-approximation

DOI10.1016/0021-9045(88)90041-XzbMath0642.42023MaRDI QIDQ1101637

Franz Peherstorfer

Publication date: 1988

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

zbMATH Keywords

orthogonal polynomialsweight\(L_ 1\)-approximationminimizing polynomialsPosse's problem

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Approximation by polynomials (41A10)

Related Items (13)

On the \(L^1\) extremal problem for entire functions ⋮ Interlacing properties of zeros of associated polynomials ⋮ Minimal polynomials for compact sets of the complex plane ⋮ Explicit generalized Zolotarev polynomials with complex coefficients ⋮ On Bernstein-Szegö orthogonal polynomials on several intervals. II: Orthogonal polynomials with periodic recurrence coefficients ⋮ On the connection of Posse's \(L_ 1\)- and Zolotarev's maximum-norm problem ⋮ Algebraic solution of a problem of E. I. Zolotarev and N. I. Akhiezer on polynomials with smallest deviation from zero ⋮ Chebyshev polynomials for disjoint compact sets ⋮ On the asymptotic behaviour of functions of the second kind and Stieltjes polynomials and on the Gauss-Kronrod quadrature formulas ⋮ Convergence of Lagrange interpolation processes based on a new systems of nodes ⋮ Orthogonal- and Chebyshev polynomials on two intervals ⋮ On polynomial preconditioning and asymptotic convergence factors for indefinite Hermitian matrices ⋮ Orthogonal and extremal polynomials on several intervals

Cites Work

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• Trigonometric polynomial approximation in the L1-norm
• Padé-type approximation and general orthogonal polynomials
• On a sufficient condition in \(L^ 1-\)approximation
• Best Approximation in an Asymmetrically Weighted L₁ Measure
• The Zeros of Certain Jacobi Polynomials
• Approximation in the Metric of L 1 (X,μ)
• Simplified Treatment of Integrals of Cauchy Type, the Hilbert Problem and Singular Integral Equations. Appendix: Poincaré-Bertrand Formula

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