Abstract
Let A = A * ∈ M n and \({\cal L} = \{ (U_k, \lambda_k)|\; U_k \in {\mathbb{C}}^n, ||U_k|| = 1\) and λ k ∈ ℝ } for k = 1,⋯,n be the set of eigenpairs of A. In this paper we develop a modified Newton method that converges to a point in \(\cal L\) starting from any point in a compact subset \({\cal D} \subseteq {\mathbb{C}}^{n+1}, {\cal L} \subseteq {\cal D}\!\).
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Datta, K., Hong, Y., Lee, R.B.: Parameterized Newton’s iteration for computing an Eigenpairs of a Real Symmetric Matrix in an Interval. Computational Methods in Applied Mathemaics 3, 517–535 (2003)
Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)
Ortega, J.M.: Numerical Analysis, A Second Course. SIAM Series in Classical in Applied Mathematics. SIAM Publications, Philadelphia (1990)
Ortega, J.M., Rheinboldt, W.C.: Iterative Solution Of Nonlinear Equations In Several Variables. Academic Press, New York (1970)
Royden, H.L.: Real Analysis. Macmillan Publishing Company, New York (1968)
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Baik, R., Datta, K., Hong, Y. (2005). Computing for Eigenpairs on Globally Convergent Iterative Method for Hermitian Matrices. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J.J. (eds) Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science, vol 3514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11428831_1
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DOI: https://doi.org/10.1007/11428831_1
Publisher Name: Springer, Berlin, Heidelberg
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