Linear rational interpolation and its application in approximation and boundary value problems

DOI10.1216/rmjm/1030539685zbMath1032.65016OpenAlexW2076470744MaRDI QIDQ1415035

Jean-Paul Berrut, Hans D. Mittelmann

Publication date: 3 December 2003

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/Vol32-2/CONT32-2/CONT32-2.html

zbMATH Keywords

algorithmsnumerical resultspseudospectral methodlinear rational interpolationlinear rational collocationpole optimization

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Approximation by rational functions (41A20) Numerical interpolation (65D05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05)

Uses Software

• simannf90

Cites Work

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• Matrices for the direct determination of the barycentric weights of rational interpolation
• Placement of cuts in Padé-like approximation
• Spectral elements for transport-dominated equations
• Lebesgue constant minimizing linear rational interpolation of continuous functions over the interval
• The barycentric weights of rational interpolation with prescribed poles
• The linear rational pseudospectral method with preassigned poles
• Rational interpolation through the optimal attachment of poles to the interpolating polynomial
• The errors in calculating the pseudospectral differentiation matrices for Čebyšev-Gauss-Lobatto points
• Improving the accuracy of the matrix differentiation method for arbitrary collocation points
• Polynomial Interpolation: Lagrange versus Newton
• Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm—Corrigenda for this article is available here
• A Collocation Solver for Mixed Order Systems of Boundary Value Problems
• Exponential convergence of a linear rational interpolant between transformed Chebyshev points
• Boundary Layer Resolving Pseudospectral Methods for Singular Perturbation Problems
• Lagrangian Interpolation at the Chebyshev Points xn,     cos (  /n),   = 0(1)n; some Unnoted Advantages
• The linear rational collocation method

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