Bidiagonal Decompositions of Vandermonde-Type Matrices of Arbitrary Rank
Numerical Analysis
2022-10-20 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2210.10148,
title = {Bidiagonal Decompositions of Vandermonde-Type Matrices of Arbitrary Rank},
author = {Jorge Delgado and Plamen Koev and Ana Marco and Jose-Javier Martinez and Juan Manuel Pena and Per-Olof Persson and Steven Spasov},
journal= {arXiv preprint arXiv:2210.10148},
year = {2022}
}