Summary
We present a method for the determination of eigenvalues of a symmetric tridiagonal matrix which combines Givens' Sturm bisection [4, 5] with interpolation, to accelerate convergence in high precision cases. By using an appropriate root of the absolute value of the determinant to derive the interpolation weight, results are obtained which compare favorably with the Barth, Martin, Wilkinson algorithm [1].
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References
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Bernstein, H.J. An accelerated bisection method for the calculation of eigenvalues of a symmetric tridiagonal matrix. Numer. Math. 43, 153–160 (1984). https://doi.org/10.1007/BF01389644
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DOI: https://doi.org/10.1007/BF01389644