Bidiagonal decompositions of Vandermonde-type matrices of arbitrary rank
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 totall...
| Authors: | , , , , , , |
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| Format: | article |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universidad de Alcalá (UAH) |
| Repository: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Language: | English |
| OAI Identifier: | oai:ebuah.uah.es:10017/60008 |
| Online Access: | http://hdl.handle.net/10017/60008 https://dx.doi.org/10.1016/j.cam.2023.115064 |
| Access Level: | Open access |
| Keyword: | Vandermonde matrix Totally nonnegative matrix Bidiagonal decomposition Eigenvalue Matemáticas Mathematics |
| Summary: | 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. |
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