A new rank estimator using Haar wavelets and the minimum description length criterion

This paper presents a rank estimator for triangular matrices employing the Haar wavelet scaling function for the analysis of the estimated smallest singular values of the principal submatrices. The wavelet transform can be computed with algorithms that have a speed comparable to the FFT algorithms making this kind of transform an ideal candidate to problems where computation speed is an issue. The resulting rank estimator is subsequently applied to the computation of the greatest common divisor of two polynomials contaminated by noise. The introduced rank estimator appears as an alternative to previous rank estimators, which, lack of a good computational efficiency when they are used in the greatest common divisor computation.