## Advances on Computer Mathematics and Its ApplicationsThis volume contains selected papers of the proceedings of the first Hellenic Conference on Mathematics and Informatics (HERMIS '92). The main theme for HERMIS '92 Conference was Computer Mathematics, with special emphasis on Computational Mathematics, Operational Research and Statistics, and Mathematics in Economic Science. The presented papers of the HERMIS Conference have been classified into the following technical sessions: Numerical solution of Differential Equations, Parallel Processing and Parallel Algorithms, Optimization and Approximation, Algorithms in Operational Research and Control Theory, Statistical Methods and Analysis, Mathematics in Economic Science, Artificial Intelligence and Data Bases Technology.In addition, a number of selected research articles published recently in the Hellenic Mathematical Society Bulletin in the form of special issues on Computer Mathematics (Volumes 31 and 32) are also included. |

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### Contents

A Dual Algorithm with Multiple Constraint Additions | 22 |

On the Computation of Zeros and Turning Points of Bessel Functions | 53 |

Approximate Solution of O D E s in Banach Space Rational | 73 |

Efficient RungeKutta Methods for Hamiltonian Equations | 107 |

Euclids Algorithm and Accelerated Iterative Methods | 125 |

An Efficient Finite Element Method for Nonlinear Diffusion | 150 |

Generalized Stability of Difference Method for Nonlinear Initial | 167 |

An eUniformly Convergent NonConforming Finite Element | 177 |

Parallel Algorithms in Numerical Linear Algebra | 211 |

The Numerical Solution of Large Finite Element Systems | 237 |

Integrated Portable Problem Solving Environments for | 257 |

A SubdomainbySubdomain Conjugate Gradient Method | 272 |

Parallel Algorithms for Integer Factorisation | 288 |

Keeping Optimality in Algorithms | 296 |

Visualizing Mathematics and Computation | 304 |

Numerical Computations for Solidification Problems with Change | 319 |

### Common terms and phrases

active set analytic applying assume asymptotic basis functions basis set blow-up boundary bounded calculation Chebychev coefficient matrix components conformal map consider constant constraints convergence corresponding defined denote derived diagonal differential equations discrete domain E-algorithm E-parameters efficient elliptic error explicit factorisation factorization Figure finite element method formula given implementation initial inner products integer Inverse Matrix iterative methods iterative scheme Karmarkar's algorithm Lagrange multipliers Lemma linear systems log barrier method Math Mathematics mesh multiple Newton's method nonlinear Schrodinger equation norm numerical results numerical solution obtained Odd-Even operations optimal parameter piecewise polynomial preconditioned methods preconditioner present problem procedure processors quadratic programming Quadratic Sieve quadrature recursive reduced respectively Runge-Kutta methods satisfy Section singularities solving space stability Step stride subdomains subsidy symmetric symplectic Table techniques Theorem torus tridiagonal tridiagonal matrix unique updating values variables vector zero