Hatem M. Khalil

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Computer science is a young field whic h is undergoing rapid change compared t o more established academic disciplines . This movement has led to a variety o f curricular approaches . Moreover, th e different environments in which compute r science has grown up . and the sundr y research interests of faculties ha s encouraged different courses of study .(More)
Least squares support vector machines (LS-SVM) based on a group of different kernel functions (Linear-Polynomial-Radial Basis Function- Exponential Radial Basis Function) for modeling nonlinear systems is introduced in this paper. A method for selecting the hyperparameters of LS-SVM is presented in details for both the regularization parameter (γ)(More)
Symbolic computation has been used to generate classes of numeric algorithms for solving linear partial differential equations A two-phase procedure is described for automatically producing multiparameter families of difference approximations to the heat operator. In the first phase, a truncated series expansion is used to form the appropriate difference(More)
This session includes three papers related to the development of algorithms for mathematical software. The first paper reports on efforts to develop software for evaluation of the square root function in microprocessors utilizing fixed point computation. The second describes the use of a simple Fortran precompiler which facilitates the use of a mathematical(More)
Let M be a square matrix of order Nn. Partition M into N 2 square matrices M(A, B), 1 < A, B < N, of order n; and let M(A, B; i , j ) , 1 < i,j < n, denote the element in the ith row and j th column o f M ( A , B). In general, for large values of Nn the problem of determining the eigenvalues and eigenvectors can only be solved by extensive calculation. For(More)
We review current work in analytic computational complexity of sequential algorithms for partial differential equations. Included are studies which analyze and compare classes of algorithms for hyperbolic, elliptic and parabolic problems. Emphasis is on the criteria and techniques used to perform the analysis and comparisons.
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