2010
DOI: 10.1007/s11075-010-9373-1
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Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave

Abstract: We have implemented in Matlab/Octave two fast algorithms for bivariate Lagrange interpolation at the so-called Padua points on rectangles, and the corresponding versions for algebraic cubature.

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Cited by 26 publications
(30 citation statements)
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“…In order to simulate the Xu points as well as the Padua points, the numerical algorithms presented in [6,9] are used. The maximum interpolation errors are computed on a uniform grid of 100×100 points defined in a region = [0, 1]×[0, 1].…”
Section: A Simple and Efficient Scheme For The Computation Of The Intmentioning
confidence: 99%
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“…In order to simulate the Xu points as well as the Padua points, the numerical algorithms presented in [6,9] are used. The maximum interpolation errors are computed on a uniform grid of 100×100 points defined in a region = [0, 1]×[0, 1].…”
Section: A Simple and Efficient Scheme For The Computation Of The Intmentioning
confidence: 99%
“…Listing 1 Matlab/Octave code for a fast computation of the coefficients C n, p of the interpolating polynomial L n, p f from the data matrix G f 1 function C = LScfsfft (n ,p , G ) 2 % Input n , p : parameters of Lissajous curve 3 % G : (2 n +2 p +1) x (2 n +1) data matrix 4 % Output C : (2 n +2 p +1) x (2 n +1) coefficient matrix Remark 4 The matrix formulations in (19) and (20) are almost identical to the formulation of the interpolating scheme of the Padua points given in [6,8]. Also, the fast algorithm for the computation of the coefficients C n, p presented in Listing 1 is a modification of a respective algorithm developed for the Padua points in [6].…”
mentioning
confidence: 99%
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“…As the points for the discrete inner product we use Padua points. The software for working with Padua points is described in [8].…”
Section: Numerical Experimentsmentioning
confidence: 99%
“…[3,5,9,10]. They are the first known optimal nodal set for total-degree multivariate polynomial interpolation, with a Lebesgue constant increasing like (log n) 2 , n being the polynomial degree.…”
Section: Introductionmentioning
confidence: 99%