Are there special methods to get exact eigenvalues of a tridiagonal matrix?
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2$\begingroup$ mathoverflow.net/questions/131527/… $\endgroup$– András BátkaiCommented Sep 25, 2017 at 16:35
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3$\begingroup$ math.stackexchange.com/questions/955168/… $\endgroup$– András BátkaiCommented Sep 25, 2017 at 16:36
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$\begingroup$ It is easier when the matrix is also Toeplitz. $\endgroup$– Rodrigo de AzevedoCommented Sep 27, 2017 at 6:43
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1 Answer
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Yes. For general tridiagonal matrices, see The Numerical Recipes, Chapter 11, or Golub-Van Loan. For symmetric tridiagonal matrices, you can do better, see Coakley/Rochlin's paper.
Coakley, Ed S.; Rokhlin, Vladimir, A fast divide-and-conquer algorithm for computing the spectra of real symmetric tridiagonal matrices, Appl. Comput. Harmon. Anal. 34, No. 3, 379-414 (2013). ZBL1264.65051.
Golub, Gene; Van Loan, Charles F., Matrix computations., Baltimore, MD: The Johns Hopkins Univ. Press. xxvii, 694 p. (1996). ZBL0865.65009.
answered Sep 25, 2017 at 16:34
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$\begingroup$ Is there something about nonsymmetric tridiagonal matrices in Golub-Van Loan? I thought not. $\endgroup$ Commented Mar 2, 2018 at 11:26