Applications of Symbolic computation in MATLAB

Symbolic computation of the Duggal transform

Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...

Introduction to Symbolic Computation: a Maple/MATLAB Course

Virtually every student who chooses to learn how to do computations on a computer ends up taking a course in numerical analysis. Compared to numerical analysis, the field of computer algebra is relatively young and has fewer active researchers. The commercial success of systems like Maple combined with the obvious wider range of applications (again compared to numerical computations) show an en...

Successful pedagogical applications of symbolic computation

The Kharitonov theorem and its applications in symbolic mathematical computation †

The Kharitonov theorem provides a means of performing sensitivity analysis for the complex roots of polynomials whose coefficients (in power base) are perturbed. In particular, it gives a computationally feasible algorithm for testing if the roots remain contained on the left hand side of the Gaussian plane if one perturbes each coefficient of a monic polynomial by a given amount. We survey an ...

Challenges of Symbolic Computation

The success of the symbolic mathematical computation discipline is striking. The theoretical advances have been continuous and significant: Gröbner bases, the Risch integration algorithm, integer lattice basis reduction, hypergeometric summation algorithms, etc. From the beginning in the early 1960s, it has been the tradition of our discipline to create software that makes our ideas readily ava...