Although optimizing transformations have been studied for over two decades, the interactions between them is not well understood. This is particularly important for the success of parallelizing compilers. In order to deal with interactions, we view loop transformations as multiplication by a suitable matrix. The transformations considered are loop interchange, permutation, reversal, hyperplane ...

Unitary operations are a specific class of linear transformations that have become an essential ingredient for the realization classical and quantum information processing. The ability implementing any n-dimensional unitary signal transformation by using reconfigurable optical hardware has recently led to pioneering concept programmable processor, whose basic building block (BB) must be correct...

A four-dimensional matrix transformation is said to be regular if it maps every bounded-convergent double sequence into a convergent sequence with the same limit. Firstly, Robison [G.M. Robison, Divergent double sequences and series, Trans. Amer. Math. Soc. 28 (1926) 50–73] presented the necessary and sufficient conditions for regular matrix transformations of double sequences. In this paper, t...

Although optimizing transformations have been studied for over two decades, the interactions between them is not well understood. This is particularly important for the success of parallelizing compilers. In order to deal with interactions, we view loop transformations as multiplication by a suitable matrix. The transformations considered are loop interchange, permutation, reversal, hyperplane ...