Symbolic computation in applied computational mechanics

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...

Computational Mathematics, Computational Logic, and Symbolic Computation (Invited Lecture)

“Computational mathematics” (algorithmic mathematics) is the part of mathematics that strives at the solution of mathematical problems by algorithms. In a superficial view, some people might believe that computational mathematics is the easy part of mathematics in which trivial mathematics is made useful by repeating trivial steps sufficiently many times on current powerful machines in order to...

Supporting Creativity in Symbolic Computation

For many people, creativity and computers are contradictory concepts: how can novel concepts arise in a machine which is designed to only do what it is programmed to do? In this paper, I give a computational model of at least one form of creativity and describe how the processes underlying it can be implemented in symbolic computation. Finally, I discuss the lessons that can be learned from the...

Merging Sub-symbolic and Symbolic Computation

In a recent short paper and a report (see [Neto et al. 98] and [Neto and Costa 99]) it was shown that programming languages can be translated efficiently on recurrent (analog, rational weighted) neural nets, using bounded resources. This fact was achieved by creating a neural programming language called NETDEF, such that each program corresponds to a modular neural net that computes it. This fr...

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