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A $ n \times n $ matrix $A$ is a tridiagonal symmetric marix such that its diagonal entries are all 2 except the final $n \times n$ element which is 1 and its superdiagonal and subdiagonal elements are all -1.

Is there any analytic method to find its eigenvalues?

I know how to find the eigenvalues of this type matrix when the last element is alos 2 by solving corresponding linear recurrence euation as in

http://www.cems.uvm.edu/~tlakoba/math337/proof_eigensystem_tridiagonal.pdf

But the same method seems to be fail in my case.

Thank you in advance.

1 Answers 1

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I found a reference by myself.

http://ac.els-cdn.com/S037704270600015X/1-s2.0-S037704270600015X-main.pdf?_tid=01a65328-48bf-11e2-a14f-00000aab0f27&acdnat=1355799777_5ff3c47f8f733ebe6d5e64758f14e942

Hope this be a help for someone else.