On the application of different numerical methods

Four different algorithms are designed to obtain the null-space of a polynomial matrix. In this first part we present two algorithms. These algorithms are based on classical methods of numerical linear algebra, namely the reduction into the column echelon form and the LQ factorization. Both algorithms take advantage of the block Toeplitz structure of the Sylvester matrix associated with the polynomial matrix. We present a full comparative analysis of the performance of both algorithms and also a brief discussion on their numerical stability.

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