A note on the stability of Toeplitz matrix inversion formulas
Copyright policy )A note on the stability of Toeplitz matrix inversion formulas
It is shown that the algorithms of \textit{A. Ben-Artzi} and \textit{T. Shalom} [Linear Algebra Appl. 75, 173--192 (1986; Zbl 0586.15005)], \textit{G. Labahn} and \textit{T. Shalom} [ibid. 175, 143--158 (1992; Zbl 0760.15005)] and \textit{M. K. Ng, K. Rost} and \textit{Y.-W. Wen} [ibid. 348, No. 1--3, 145--151 (2002; Zbl 0998.15031)] for the inversion of a well conditioned Toeplitz matrix are forward stable. I.e., the difference between the computed inverse and the exact inverse has a finite \(2\)-norm.
- Chinese Academy of Sciences China (People's Republic of)
- University of Hong Kong China (People's Republic of)
- University of Hong Kong (香港大學) China (People's Republic of)
- Institute of Geology and Geophysics China (People's Republic of)
Applied Mathematics, Forward stable, Theory of matrix inversion and generalized inverses, Toeplitz matrix, inversion formulas, stability, Direct numerical methods for linear systems and matrix inversion, Stability, forward stable, Inversion formulas
Applied Mathematics, Forward stable, Theory of matrix inversion and generalized inverses, Toeplitz matrix, inversion formulas, stability, Direct numerical methods for linear systems and matrix inversion, Stability, forward stable, Inversion formulas
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