Ten lectures on wavelets
On the computation of Battle-Lemarie´'s wavelets
Mathematics of Computation
Spectral Factorizations and Sums of Squares Representations via Semidefinite Programming
SIAM Journal on Matrix Analysis and Applications
On the Cholesky Factorization of the Gram Matrix of Multivariate Functions
SIAM Journal on Matrix Analysis and Applications
Tight wavelet frames via semi-definite programming
Journal of Approximation Theory
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Recently Dritschel proved that any positive multivariate Laurent polynomial can be factorized into a sum of square magnitudes of polynomials. We first give another proof of the Dritschel theorem. Our proof is based on the univariate matrix Fejér-Riesz theorem. Then we discuss a computational method to find approximates of polynomial matrix factorization. Some numerical examples will be shown. Finally we discuss how to compute nonnegative Laurent polynomial factorizations in the multivariate setting.