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Algorithm 886: Padua2D---Lagrange Interpolation at Padua Points on Bivariate Domains

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 35 , Issue 3 (October 2008) table of contents

Article No. 21

Year of Publication: 2008

ISSN:0098-3500

Authors

Marco Caliari	University of Verona
Stefanode Marchi	University of Verona
Marco Vianello	University of Padua

Publisher

ACM New York, NY, USA

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Software for Padua2D---Lagrange Interpolation at Padua Points on Bivariate Domains

ABSTRACT

We present a stable and efficient Fortran implementation of polynomial interpolation at the Padua points on the square [ − 1,1]². These points are unisolvent and their Lebesgue constant has minimal order of growth (log square of the degree). The algorithm is based on the representation of the Lagrange interpolation formula in a suitable orthogonal basis, and takes advantage of a new matrix formulation together with the machine-specific optimized BLAS subroutine for the matrix-matrix product. Extension to interpolation on rectangles, triangles and ellipses is also described.

REFERENCES

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