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In this paper, we conjecture a formula for the value of the Pythagoras number for real multivariate sum of squares polynomials as a function of the (total or coordinate) degree and the number of variables. The conjecture is based on the comparison between the number of parameters and the number of conditions for a corresponding low-rank representation. This… (More)

- Thanh Hieu Le, Marc Van Barel
- J. Computational Applied Mathematics
- 2014

In this paper, we formulate the feasibility problem corresponding to a filter design problem as a convex optimization problem. Combined with a bisection rule this leads to an algorithm of minimizing the design parameter in the filter design problem. A safety margin is introduced to solve the numerical difficulties when solving this type of problems… (More)

This paper presents lower and upper bounds on the Pythagoras number of sum of square magnitudes of complex polynomials using well-known results on a system of quadratic polynomial equations. Applying this method, a new proof for the upper bound of the Pythagoras number of real polynomials is also presented.

- Thanh Hieu Le, Marc Van Barel
- Numerical Algorithms
- 2014

This paper presents an algorithm for computing a decomposition of a non-negative real polynomial as a sum of squares of rational functions. Rational functions in our algorithm have the denominators that are powers of the sum of squares of coordinate functions. Numerical experiments are performed for several well-known polynomials such as Motzkin… (More)

- Thanh Hieu Le, Marc Van Barel
- J. Computational Applied Mathematics
- 2016

- Micol Ferranti, Thanh Hieu Le, Raf Vandebril
- Numerical Algorithms
- 2013

An algorithm for computing the singular value decomposition of normal matrices using intermediate complex symmetric matrices is proposed. This algorithm, as most eigenvalue and singular value algorithms, consists of two steps. It is based on combining the unitarily equivalence of normal matrices to complex symmetric tridiagonal form with the symmetric… (More)

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