The Need for and the Advantages of Generalized Tensor Algebra for Kronecker Structured Representations
Léonardo Brenner, Paulo Fernandes · 2005
This paper presents the advantages in extending Classical Tensor Algebra (CTA), also known as Kronecker Algebra, to allow the definition of functions, i.e., functional dependencies among its operands. Such extended tensor algebra have been called Generalized Tensor Algebra (GTA). Stochastic Automata Networks (SAN) and Superposed Generalized Stochastic Petri Nets (SGSPN) formalisms use such Kronecker representations. The advantages of GTA do not imply in a reduction or augmentation of application scope, since there is a representation equivalence between SAN, which uses GTA, and SGSPN, which uses only CTA. Two modeling examples are presented in order to draw comparisons between the memory needs and CPU time required for the generation and solution using both formalisms, showing the computational advantages in using GTA.