Multivariate Vandermonde matrices with separated nodes on the unit circle are stable
نویسندگان
چکیده
We prove explicit lower bounds for the smallest singular value and upper condition number of rectangular, multivariate Vandermonde matrices with scattered nodes on complex unit circle. Analogously to Shannon-Nyquist criterion, are assumed be separated by a constant divided used polynomial degree. If this grows linearly spatial dimension, is uniformly bounded. it only logarithmically can, in worst case, grow slightly stronger than exponentially dimension. Both results improve over all previously known such type cannot improved considerably which shown considering specific node sets.
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2022
ISSN: ['1096-603X', '1063-5203']
DOI: https://doi.org/10.1016/j.acha.2022.01.001