Complete numerical isolation of real zeros in zero-dimensional triangular systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Complexity of real root isolation using continued fractions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
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In statistical signal processing problems involving second-order information of data such as covariance estimation, spectral factorization, and optimal filtering, one often needs to test positivity of a real sequence obtained from the finite length of data as covariance estimates. In this correspondence, we present efficient time-domain algorithms for testing nonnegativity of real finite nonparametric and linearly parametric sequences as valid covariance estimates. For a parametric sequence, the algorithm searches entire parameter space to find a unique set of parameters for which the sequence is positive-definite. Examples show performance of the proposed algorithms versus direct use of DFT/FFT.