Abstract
The objective of this research is the presentation of a neural network capable of solving complete nonlinear algebraic systems of n equations with n unknowns. The proposed neural solver uses the classical back propagation algorithm with the identity function as the output function, and supports the feature of the adaptive learning rate for the neurons of the second hidden layer. The paper presents the fundamental theory associated with this approach as well as a set of experimental results that evaluate the performance and accuracy of the proposed method against other methods found in the literature.
Highlights
The estimation of the roots associated with nonlinear algebraic systems has been a major area of research in applied mathematics [1] as well as in other disciplines and fields of human knowledge such as physics [2], chemistry [3], economics [4], engineering [5], mechanics, medicine and robotics
To examine and test the validity and the accuracy of the proposed method, sample nonlinear algebraic systems were selected and solved using the neural network approach and the results were compared against those obtained from other methods
The adaptive learning rate approach (ALR) is considered as the primary algorithm, but the network is tested with a fixed learning rate (FLR) value
Summary
The estimation of the roots associated with nonlinear algebraic systems has been a major area of research in applied mathematics [1] as well as in other disciplines and fields of human knowledge such as physics [2], chemistry [3], economics [4], engineering [5], mechanics, medicine and robotics. The novel feature of the proposed method is the adaptive learning rate that allows the neural processing elements of a layer to work under different conditions. Another interesting feature of the presented neural solver is the fact that the components of the identified roots are not associated with the outputs of the neural network, as in other methods but with the weights of the synapses joining the first and the second layer. These results are compared against those emerged by applying other methods and the accuracy and the performance of the proposed neural solver are evaluated.
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