## Advances in Numerical Partial Differential Equations and Optimization: Proceedings of the Fifth Mexico-United States WorkshopThe papers in this volume emphasize the numerical aspects of three main areas: optimization, linear algebra and partial differential equations. Held in January, 1989, in Yucatan, Mexico, the workshop was organized by the Institute for Research in Applied Mathematics of the National University of Mexico in collaboration with the mathematical Sciences Department at Rice University. |

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### Contents

Allen Department of Mathematics Texas AM University College Station TX 77843 | 5 |

A Simulated | 9 |

Polyhedral Invariants and a Representative Theorem in Projective | 43 |

Towards a Theory of Optimization in Projective Space | 50 |

Iterative GradientNewton Type Methods for Steady Shock | 60 |

Diaz Center for Parallel and Scientific Computing University of Tulsa Tulsa | 76 |

Approximate Inverse Preconditioning for Nonsymmetric Sparse | 101 |

On Generalized Finite Difference Methods for Approximating | 112 |

Layne T Watson Department of Computer Science Virginia Polytechnic Institute State | 198 |

LargeScale Extended LinearQuadratic Programming and Multistage | 247 |

A Finite Difference Approach to the KuramotoSivashinsky Equation | 262 |

Francesco Zurilli Dipartimento di Matematica G Castelnuovo Universita di Roma | 273 |

The Application of Globally Convergent Homotopy Methods | 284 |

Gay ATT Bell Laboratories Murray Hill NJ 079742070 | 299 |

Two Second Order Regularization Methods to Solve the Finite | 320 |

Gonglewski U S Air Forces Weapons Laboratory Optical Phased Array Branch | 332 |

Romero Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas Universidad | 141 |

Problem | 158 |

A New Discrete Functional for Grid Generation | 185 |

An Approach to Nonlinear Approximation | 346 |

### Common terms and phrases

algorithm applications approximate inverse boundary conditions bounded operator cadre cell computed consider constraints convex set corresponding defined denotes desired eigenvalues diagonal differential equations diffusion dimensional discrete dual eigenvalue approximations EIGENVALUES Figure eigenvector EISPACK error estimates finite difference finite element methods flux formulation Frobenius norm function geometry given gradient Hennart homotopy inverse iteration iterative method L2 norm Lagrange multipliers Lagrangian Lanczos matrices Lanczos procedures Lanczos vectors Lemma linear programming linear system linesearch Math MHD example minimization mixed-hybrid nonlinear nonsymmetric norm obtained optimal solution oriented matroids original matrix parameter piecewise plotted by number polyhedral polynomial preconditioner preconditioning primal projective proof quadratic programming R.E. EWING real symmetric recursion reorthogonalization schemes SHFTOL shift and invert shifts plotted si/e SIAM solving space sparse spectrum step subspace superconvergence Table techniques Test Theorem tion transport equation tridiagonal tridiagonal matrix update upwind values variables weakly converged zero