  The backpropagation algorithm, which had been originally introduced in the
1970s, is the workhorse of learning in neural networks. This backpropagation
algorithm makes use of the famous machine learning algorithm known as Gradient
Descent, which is a first-order iterative optimization algorithm for finding
the minimum of a function. To find a local minimum of a function using gradient
descent, one takes steps proportional to the negative of the gradient (or of
the approximate gradient) of the function at the current point. In this paper,
we develop an alternative to the backpropagation without the use of the
Gradient Descent Algorithm, but instead we are going to devise a new algorithm
to find the error in the weights and biases of an artificial neuron using
Moore-Penrose Pseudo Inverse. The numerical studies and the experiments
performed on various datasets are used to verify the working of this
alternative algorithm.
