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In this paper we consider IIR filter design where both magnitude and phase are optimized using a weighted and sampled least-squares criterion. We propose a new convex stability domain defined by positive realness for ensuring the stability of the filter and adapt the Steiglitz-McBride (SM), Gauss-Newton (GN) and classical descent methods to the new… (More)

Several results in systems and signal theory can be derived in a unified fashion from polynomial positivity conditions, and handled numerically with semidefinite programming, a broad generalization of linear programming to the cone of positive semidefinite matrices. Results in the area bridge gaps between algebra, geometry, optimization and engineering.… (More)

The problem of training a dictionary for sparse representations from a given dataset is receiving a lot of attention mainly due to its applications in the fields of coding, classification and pattern recognition. One of the open questions is how to choose the number of atoms in the dictionary: if the dictionary is too small then the representation errors… (More)

We propose a characterization of multivariate trigonometric polynomials that are positive on a given frequency domain. The positive polynomials are parameterized function of sum-of-squares polynomials and so semidefinite programming (SDP) is applicable. The frequency domain is expressed via the positivity of some trigonometric polynomials. We also give a… (More)

- Tae Roh, Bogdan Dumitrescu, Lieven Vandenberghe
- 2007

We discuss a method for multidimensional FIR filter design via sum-of-squares formulations of spectral mask constraints. The sum-of-squares optimization problem is expressed as a semidefinite program with low-rank structure, by sampling the constraints using discrete cosine and sine transforms. The resulting semidefinite program is then solved by a… (More)

Sequential fast matrix multiplication algorithms of Strassen and Winograd are studied ; the complexity bound given by Strassen is improved. These algorithms are parallelized on MIMD distributed memory architectures of ring and torus topologies; a generalization to a hyper-torus is also given. Complexity and efficiency are analyzed and good asymptotic… (More)

A new stability test for d-dimensional systems is presented. It consists of maximizing the minimum eigenvalue of a positive definite Gram matrix associated with a polynomial positive on the unit d-circle. This formulation is based on expressing the polynomial as a sum of squares and leads to a semidefinite programming (SDP) problem, which may be solved… (More)