Pavel Dourbal

Pavel Dourbal, Mikhail Pekker

A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with conventional numerical methods. It was shown that the new method allows for linear growth in the number of elementary addition and multiplication operations with the growth of grid size, as contrasted with quadratic growth necessitated by the standard numerical methods. The proposed method can be easily generalized for any differential equations.

Pavel Dourbal, Mikhail Pekker

Computationally efficient classification system architecture is proposed. It utilizes fast tensor-vector multiplication algorithm to apply linear operators upon input signals . The approach is applicable to wide variety of recognition system architectures ranging from single stage matched filter bank classifiers to complex neural networks with unlimited number of hidden layers.