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Kitakado, Masaharu
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Astronomy Chemistry Earth & Planetary Sciences Mathematics Physics

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Discretization and Associated Asymptotic Behavior for the Lax Equation with Skew-symmetry Shinjo, Masato; Kitakado, Masaharu
Journal of Mathematical and Fundamental Sciences Vol. 56 No. 3 (2024)
Publisher : Directorate for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2024.56.3.4

Abstract

The computation of matrix eigenvalues is vital for understanding various scientific phenomena. The QR method, which is based on the QR factorization of a matrix, is a common approach in numerical linear algebra. In integrable systems, the one-step process of the QR method is related to the time evolution of the Lax equation. In this paper, we clarify the relationship between the QR method, which incorporates an origin shift parameter, and the Lax equation with skew-symmetry. Furthermore, we show the asymptotic convergence of discretization based on matrix factorization of the Lax equation with skew-symmetry as discrete time approaches infinity.
Co-Authors Shinjo, Masato