Computing the Minimum Eigenvalue of a Symmetric Positive Definite Toeplitz Matrix
George V. Cybenko, Charles F. Van Loan · SIAM Journal on Scientific and Statistical Computing · 1986
A method for computing the smallest eigenvalue of a symmetric positive definite Toeplitz matrix is given. It relies solely upon the Levinson–Durbin algorithm. The procedure involves a combination of bisection and Newton’s method. Good starting values are also shown to be obtainable from the Levinson–Durbin algorithm.