Publication Date
7-1-2023
Document Type
Article
Publication Title
Journal of Computational and Applied Mathematics
Volume
426
DOI
10.1016/j.cam.2023.115064
Abstract
We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) Bernstein-Vandermonde ones, among others. These results generalize the existing expressions for nonsingular matrices to matrices of arbitrary rank. For totally nonnegative matrices of the above classes, the new decompositions can be computed efficiently and to high relative accuracy componentwise in floating point arithmetic. In turn, matrix computations (e.g., eigenvalue computation) can also be performed efficiently and to high relative accuracy.
Funding Number
E41-17R
Funding Sponsor
National Aeronautics and Space Administration
Keywords
Bidiagonal decomposition, Eigenvalue, Totally nonnegative matrix, Vandermonde matrix
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Mathematics and Statistics
Recommended Citation
Jorge Delgado, Plamen Koev, Ana Marco, José Javier Martínez, Juan Manuel Peña, Per Olof Persson, and Steven Spasov. "Bidiagonal decompositions of Vandermonde-type matrices of arbitrary rank" Journal of Computational and Applied Mathematics (2023). https://doi.org/10.1016/j.cam.2023.115064
Comments
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