A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Spectral Factorizations and Sums of Squares Representations via Semidefinite Programming
SIAM Journal on Matrix Analysis and Applications
Factorization of multivariate positive Laurent polynomials
Journal of Approximation Theory
Positive Trigonometric Polynomials and Signal Processing Applications
Positive Trigonometric Polynomials and Signal Processing Applications
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In this paper we state the ''oblique extension principle'' as a problem of semi-definite programming. Using this optimization technique we show that the existence of a tight frame is equivalent to the existence of a certain matrix from a cone of positive semi-definite matrices, whose entries satisfy linear constraints. We also discuss how to use the optimization techniques to reduce the number of frame generators in univariate and multivariate cases. We apply our results for constructing tight frames for several subdivision schemes.