The eigenvalue problem for infinite complex symmetric tridiagonal matrices with application (Q1923165)

The authors prove that eigenvalues of complex symmetric tridiagonal matrices with bounded off-main diagonal entries and main diagonal entries approaching infinity, are approximated by the eigenvalues of finite principal submatrices under a few hypotheses. The eigenvalue has to be simple, the inner product of the eigenvector with itself (complex bilinear inner product) is nonzero, and a ratio involving it has to approach zero. Applications to the Mathieu equation are given.