2 Eugene Allgower ,

Numerical Path Following

Piecewise Linear Approximation of Smooth Compact Fibers

Piecewise Linear Methods for Nonlinear Equations and Optimization

1. Introduction Piecewise linear algorithms, also referred to in the literature as sim-plicial algorithms, can be used to generate piecewise linear manifolds which approximate the solutions of underdetermined systems of equa

Computation of Weakly and Nearly Singular Integrals over Triangles in R3

We study the approximation of weakly singular integrals over triangles in general position in R3, giving explicit formulae where convenient and numerical quadrature in more general cases. Particular models considered concern the collocation and Galerkin methods in the boundary integral approach to the Dirichlet problem for Laplace’s equation.

On the Complexity of Exclusion Algorithms for Optimization

Exclusion algorithms are a well-known tool in the area of interval analysis for finding all solutions of a system of nonlinear equations or for finding the global minimum of a function over a compact domain. The present paper discusses a new class of tests for such algorithms in the context of global optimization, and presents complexity results concerning the resulting algorithms.