Abstract
In this paper we use the displacement structure concept to introduce a new class of matrices, designated asChebyshev-Vandermonde-like matrices, generalizing ordinary Chebyshev-Vandermonde matrices, studied earlier by different authors. Among other results the displacement structure approach allows us to give a nice explanation for the form of the Gohberg-Olshevsky formulas for the inverses of ordinary Chebyshev-Vandermonde matrices. Furthermore, the fact that the displacement structure is inherited by Schur complements leads to a fastO(n 2) implementation of Gaussian elimination withpartial pivoting for Chebyshev-Vandermonde-like matrices.
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This research was supported in part by the Army Research Office under Grant DAAH04-93-G-0029. This manuscript is submitted for publication with the understanding that the US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon.
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Kailath, T., Olshevsky, V. Displacement structure approach to Chebyshev-Vandermonde and related matrices. Integr equ oper theory 22, 65–92 (1995). https://doi.org/10.1007/BF01195490
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DOI: https://doi.org/10.1007/BF01195490