[2210.10148] Bidiagonal Decompositions of Vandermonde-Type Matrices of Arbitrary Rank
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Mathematics > Numerical Analysis

arXiv:2210.10148 (math)
[Submitted on 18 Oct 2022]

Title:Bidiagonal Decompositions of Vandermonde-Type Matrices of Arbitrary Rank

Authors:Jorge Delgado, Plamen Koev, Ana Marco, Jose-Javier Martinez, Juan Manuel Pena, Per-Olof Persson, Steven Spasov
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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.
Subjects: Numerical Analysis (math.NA)
MSC classes: 65F15, 15A23, 15B48, 15B35
Cite as: arXiv:2210.10148 [math.NA]
  (or arXiv:2210.10148v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2210.10148

Submission history

From: Plamen Koev S [view email]
[v1] Tue, 18 Oct 2022 20:27:44 UTC (37 KB)
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