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- W2902134462 abstract "Since it is well-known that the Vandermonde matrix is ill-conditioned, this paper surveys the choices of other bases. These bases are data-dependent and are categorized into discretely $ell^2$-orthonormal and continuously $L^2$-orthonormal bases. The first one is defined via a decomposition of the Vandermonde matrix while the latter is given by a decomposition of the Gramian matrix corresponding to monomial bases. A discussion of various matrix decomposition (e.g. Cholesky, QR and SVD) provides a variety of different bases with different properties. Special attention is given to duality. Numerical results show that the matrices of values of the new bases have smaller condition numbers than the common monomial bases. It can also be pointed out that the new introduced bases are good candidates for interpolation." @default.
- W2902134462 created "2018-12-11" @default.
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- W2902134462 date "2018-10-14" @default.
- W2902134462 modified "2023-09-28" @default.
- W2902134462 title "Bases for polynomial-based spaces" @default.
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- W2902134462 doi "https://doi.org/10.22124/jmm.2018.11242.1189" @default.
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