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Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

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Abstract

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N 2log2 N) andO(N 2log2log2 N) arithmetic operations, respectively.

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Bialecki, B. Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation. Numer Algor 8, 167–184 (1994). https://doi.org/10.1007/BF02142689

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Keywords

  • Poisson's equation
  • Dirichlet
  • Neumann
  • periodic boundary conditions
  • separable equations
  • piecewise Hermite cubics
  • Gauss points
  • orthogonal spline collocation
  • almost block diagonal matrices
  • Fourier analysis and cyclic reduction methods

AMS (MOS) subject classification

  • 65F05
  • 65N22
  • 65N35