On the approximation of certain functions by interpolating polynomials

DOI10.1017/S0004972700032494zbMath0934.41001MaRDI QIDQ4236679

Michael Revers

Publication date: 4 April 2000

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

interpolationorder of approximationbest approximationapproximation of \(|x|^{\alpha}\)

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)

Related Items (6)

Strong asymptotics in Lagrange interpolation with equidistant nodes ⋮ Polynomial interpolation, an \(L\)-function, and pointwise approximation of continuous functions ⋮ The divergence of Lagrange interpolation for \(|x|^\alpha\) at equidistant nodes ⋮ A highly accurate trivariate spectral collocation method of solution for two-dimensional nonlinear initial-boundary value problems ⋮ Solving hyperbolic partial differential equations using a highly accurate multidomain bivariate spectral collocation method ⋮ The Bernstein constant and polynomial interpolation at the Chebyshev nodes.

Cites Work

• On the Bernstein conjecture in approximation theory
• Approximation of powers of x by polynomials
• Chebychev coefficients in approximation of powers of \(x\)
• Rational approximation to \(|x|\)
• Oscillating polynomials and approximations to fractional powers of x
• Best uniform rational approximation of 𝑥^{𝛼} on [0,1]

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