Journal of Computational and Applied Mathematics
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.
National Aeronautics and Space Administration
Bidiagonal decomposition, Eigenvalue, Totally nonnegative matrix, Vandermonde matrix
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Mathematics and Statistics
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