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Articles by Abbas Y. Al Bayati
Total Records ( 2 ) for Abbas Y. Al Bayati
  Abbas Y. Al Bayati , Najmaddin A. Sulaiman and Gulnar W. Sadiq
  Problem statement: The Conjugate Gradient (CG) algorithm which usually used for solving nonlinear functions is presented and is combined with the modified Back Propagation (BP) algorithm yielding a new fast training multilayer algorithm. Approach: This study consisted of determination of new search directions by exploiting the information calculated by gradient descent as well as the previous search direction. The proposed algorithm improved the training efficiency of BP algorithm by adaptively modifying the initial search direction. Results: Performance of the proposed algorithm was demonstrated by comparing it with the Neural Network (NN) algorithm for the chosen test functions. Conclusion: The numerical results showed that number of iterations required by the proposed algorithm to converge was less than the both standard CG and NN algorithms. The proposed algorithm improved the training efficiency of BP-NN algorithms by adaptively modifying the initial search direction.
  Abbas Y. Al Bayati , Rostam K. Saeed and Faraidun K. Hama-Salh
  Problem statement: The lacunary interpolation problem, which we had investigated in this study, consisted in finding the six degree spline S(x) of deficiency four, interpolating data given on the function value and third and fifth order in the interval [0,1]. Also, an extra initial condition was prescribed on the first derivative. Other purpose of this construction was to solve the second order differential equations by two examples showed that the spline function being interpolated very well. The convergence analysis and the stability of the approximation solution were investigated and compared with the exact solution to demonstrate the prescribed lacunary spline (0, 3, 5) function interpolation. Approach: An approximation solution with spline interpolation functions of degree six and deficiency four was derived for solving initial value problems, with prescribed nonlinear endpoint conditions. Under suitable assumptions, the existences; uniqueness and the error bounds of the spline (0, 3, 5) function had been investigated; also the upper bounds of errors were obtained. Results: Numerical examples, showed that the presented spline function proved their effectiveness in solving the second order initial value problems. Also, we noted that, the better error bounds were obtained for a small step size h. Conclusion: In this study we treated for a first time a lacunary data (0,3,5) by constructing spline function of degree six which interpolated the lacunary data (0,3,5) and the constructed spline function applied to solve the second order initial value problems.
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