Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776646 | Applied Numerical Mathematics | 2017 | 10 Pages |
Abstract
For aâZ>0d we let âa(t):=(cosâ¡(a1t),cosâ¡(a2t),â¯,cosâ¡(adt)) denote an associated Lissajous curve. We study such Lissajous curves which have the quadrature property for the cube [â1,1]d thatâ«[â1,1]dp(x)dμd(x)=1Ïâ«0Ïp(âa(t))dt for all polynomials p(x)âV where V is either the space of d-variate polynomials of degree at most m or else the d-fold tensor product of univariate polynomials of degree at most m. Here dμd is the product Chebyshev measure (also the pluripotential equilibrium measure for the cube). Among such Lissajous curves with this property we study the ones for which maxpâVâ¡deg(p(âa(t))) is as small as possible. In the tensor product case we show that this is uniquely minimized by g:=(1,(m+1),(m+1)2,â¯,(m+1)dâ1). In the case of m=2n we construct discrete hyperinterpolation formulas which are easily evaluated with, for example, the Chebfun system ([6]).
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
L. Bos, S. De Marchi, M. Vianello,