### Solving Numerical Computation Problems Using a Few Artificial Neurons

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#### Abstract

Numerical Computation is widely used in engineering problems. In this paper, it is shown that many Numerical Computation problems can be expressed by one or few artificial neurons. Then, the task of solving each of the problems is converted to the task of training the neurons in order to find the weights of the neurons. The weights of the neurons contain the solution to the problem at hand. As a result, to solve a Numerical Computation problem, there is no need to develop special algorithms for the problem. Experimental results demonstrate that this novel approach is successful in solving several different Numerical Computation problems and may pave the way to tackle other Numerical Computation problems by using only neural networks without developing specific algorithms *Copyright © 2013 Praise Worthy Prize - All rights reserved.*

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Endre Süli and David Mayers, An Introduction to Numerical Analysis, (Cambridge University Press, 2003. ISBN 0-521-00794-1).

http://dx.doi.org/10.1017/cbo9780511801181.008

George E. Forsythe, Michael A. Malcolm, and Cleve B. Moler., Computer Methods for Mathematical Computations. (Englewood Cliffs, NJ: Prentice-Hall, 1977. (Chapter 5.))

http://dx.doi.org/10.1002/zamm.19790590235

Dormand, J. R. and P. J. Prince, A family of embedded Runge-Kutta formulae, J. Comp. Appl. Math., Vol. 6, 1980, pp 19-26.

http://dx.doi.org/10.1016/0771-050x(80)90013-3

Rosenblatt, F., The Perceptron: A probabilistic model for information storage and organization in the brain, Psychological Review, Vol. 65, 1985, pp. 386-408

http://dx.doi.org/10.1037/h0042519

Rumelhart, D. E., G. E. Hinton, and R. J. Williams, learning internal representation by error propagation, parallel distributed processing: explorations in the microstructure of cognition, (Vol.1: foundations, D. E. Rumelhart and J. L. McClelland (eds.), pp. 318-362 Cambridge, MA: MIT Press, 1986).

Rosenblatt, F., Principles of Neurodynamics, (Washington D.C., Spartan Press, 1961).

N. J. Hagan, M.T., H.B. Demuth, and M.H. Beale, Neural Network Design, Boston, (MA: PWS Publishing, 1996).

Hagan, M.T., and M. Menhaj, Training feed-forward networks with the Marquardt algorithm, IEEE Transactions on Neural Networks, Vol. 5, No. 6, 1999, pp. 989-993, 1994.

http://dx.doi.org/10.1109/72.329697

Nguyen, D., and B. Widrow, Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights, Proceedings of the International Joint Conference on Neural Networks, Vol. 3, 1990, pp. 21-26.

http://dx.doi.org/10.1109/ijcnn.1990.137819

M.J.D. Powell (1981). Approximation Theory and Method, Chapter 4. Cambridge University Press. ISBN 0-521-29514-9.

Stephen Gasiorowicz, Quantum Physics,(Wiley, 2003).

M.V.K Chari, Shepard Joel Salon, Numerical Methods in Electromagnetic, (Academic Press, 2000),

http://dx.doi.org/10.1016/b978-012615760-4/50002-x

Erkki Oja, Neural Networks, Principle Components, and Subspaces, International Journal Of Neural Systems, Vol.1, Issue Num.1, pp:61-68, 1989.

http://dx.doi.org/10.1142/s0129065789000475

Simon Haykin, Neural Networks: a Comprehensive Foundation, (Prentice-Hall, 1998.)

Hamed Shah-Hosseini and Reza Safabakhsh, TAPCA: Time Adaptive Self Organizing Maps for Adaptive Principle Components Analysis, IEEE International Conference on Image Processing, 2001, pp:509-512.

http://dx.doi.org/10.1109/icip.2001.959065

William H. Hager, Applied Numerical Linear Algebra, (Prentice-Hall, international edition ,N. Y.,1988,pp.253-260).

Philip E. Gill and Walter Murray (1978). "Algorithms for the solution of the nonlinear least-squares problem". SIAM Journal on Numerical Analysis 15 (5): 977–992. doi:10.1137/0715063

http://dx.doi.org/10.1137/0715063

S. J. Julier and J.K. Uhlmann, "A new extension of the Kalman filter to nonlinear systems," in Proc. AeroSense: 11th Int. Symp. Aerospace/Defence Sensing, Simulation and Controls, 1997, pp. 182-193

Roger A. Horn and Charles R. Johnson. Matrix Analysis, Section 7.2. Cambridge University Press, 1985. ISBN 0-521-38632-2.

Ernst Hairer, Syvert Paul Norsett and Gerhard Wanner, Solving ordinary differential equations I: Nonstiff problems, second edition, Springer Verlag, Berlin, 1993. ISBN 3-540-56670-8.

http://dx.doi.org/10.1007/978-3-662-12607-3

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