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Jacobi algorithm for symmetric eigenvalue problem and integrable gradient system of Lax form. (English) Zbl 1306.65188

Summary: An intimate connection between matrix eigenvalue algorithms and integrable dynamical systems is studied. It is proved that an infinitesimal rotation of each step of the Jacobi algorithm for symmetric eigenvalue problem is an integrable gradient system of Lax form.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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