A Method of Order 1+SQRT(3) for Computing the Smallest Eigenvalue of a Symmetric Toeplitz Matrix

Kostić, AleksandraAleksandraKostićVoß, HeinrichHeinrichVoß2006-02-272006-02-272002-03http://tubdok.tub.tuhh.de/handle/11420/162In this note we discuss a method of order 1+sqrt(3) for computing the smallest eigenvalue lambda_1 of a symmetric and positive definite Toeplitz matrix. It generalizes and improves a method introduced in cite{MacVos97} which is based on rational Hermitean interpolation of the secular equation. Taking advantage of a further rational approximation of the secular equation which is essentially for free and which yields lower bounds of lambda_1 we obtain an improved stopping criterion.enhttp://rightsstatements.org/vocab/InC/1.0/eigenvalue problemToeplitz matrixsecular equationMathematikA Method of Order 1+SQRT(3) for Computing the Smallest Eigenvalue of a Symmetric Toeplitz MatrixTechnical Report2006-03-01urn:nbn:de:gbv:830-opus-222310.15480/882.160EigenwertproblemToeplitz-MatrixEigenvalues, eigenvectors11420/16210.15480/882.160930768128Technical Report