Accurate bidiagonal decompositions of Cauchy–Vandermonde matrices of any rank
Publication Date
1-1-2024
Document Type
Article
Publication Title
Numerical Linear Algebra with Applications
DOI
10.1002/nla.2579
Abstract
We present a new decomposition of a Cauchy–Vandermonde matrix as a product of bidiagonal matrices which, unlike its existing bidiagonal decompositions, is now valid for a matrix of any rank. The new decompositions are insusceptible to the phenomenon known as subtractive cancellation in floating point arithmetic and are thus computable to high relative accuracy. In turn, other accurate matrix computations are also possible with these matrices, such as eigenvalue computation amongst others.
Funding Number
E41_23R
Funding Sponsor
Ministerio de Ciencia, Innovación y Universidades
Keywords
bidiagonal decomposition, Cauchy–Vandermonde matrix, eigenvalues, totally nonnegative matrix
Department
Mathematics and Statistics
Recommended Citation
Jorge Delgado, Plamen Koev, Ana Marco, José Javier Martínez, Juan Manuel Peña, Per Olof Persson, and Steven Spasov. "Accurate bidiagonal decompositions of Cauchy–Vandermonde matrices of any rank" Numerical Linear Algebra with Applications (2024). https://doi.org/10.1002/nla.2579
