Transfer function computation for generalized n-dimensional systems

On the numerical computation of the determinant of a bivariate polynomial matrix

“…This programming approach is described in Appendix. The third approach executes in each step of k the required iterations for each term separately by taking the advantage of the symmetry of the first and second term in the recursive formula (1). This programming approach is described in Appendix.…”

“…Polynomial interpolation in several variables is a relatively new topic that has applications to many mathematical problems where the solution is a multivariate polynomial or polynomial matrix i.e. the computation of a) the inverse of a polynomial matrix that has applications in analysis and synthesis theory of Control Systems [5,8], b) the greatest common divisor [7], c) the determinant of a polynomial matrix [9], d) the solution of Diophantine equations [4], e) the transfer function of a multidimensional system [1], f) the generalized inverse of a polynomial matrix [6] e.t.c. The analytical solution of these problems leads to difficult and complex procedures that are very difficult to implement in a programming environment which must to supports symbolic operations.…”

On a special case of the two-variable Newton interpolation polynomial

“…Polynomial interpolation plays a crucial role in a number of applications such as : the calculation of the determinantal polynomial [8], [9], the computation of the transfer function of generalized n-dimensional systems [10], the solutions of polynomial matrix Diophantine equations [11], and the computation of the inverse or the generalized inverse of multivariable polynomial matrices [12], [13], [9], [14]. The Newton multivariate polynomial interpolation can be applied both to triangular and rectangular bases.…”

Inverses of Multivariable Polynomial Matrices by Discrete Fourier Transforms

“…Some remarkable examples, but not the only ones of the use of DFT in linear algebra problems, are the calculation of the determinantal polynomial by [15], the computation of the transfer function of generalized n-dimensional systems by [1] and the solutions of polynomial matrix Diophantine equations by [9].…”

“…Note that in case of square and nonsingular matrices, both inverses coincide with the known inverse of the matrix. Therefore the computation of these special inverses gives rise also to applications where the usual inverse of a matrix is required such as the computation of the transfer function of a matrix ( [2], [1]). …”