Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado, March 29-April 4, 1998

研究人员和他的同事组织了一次会议，专门讨论线性和非线性方程组的迭代解法。特别的主题是非对称线性系统，非线性系统的全局收敛算法，最优工作顺序算法，鞍点问题，以及在多处理器计算机体系结构上的应用。对现实世界问题的数学描述不可避免地导致需要求解的方程。很多时候这些方程是非线性的，因为潜在的问题是非线性的。然而，通常最初的问题是线性的，数学方程也是线性的。这些问题出现在所有的科学和技术领域，在生物学、材料、环境研究和制造业中特别有趣。这些领域的进展需要解决更全面的建模方程——这样的模型通常比简单的模型更非线性——或者更精确地解决现有模型——增加待解决的数值问题的规模。在某些问题中，特别是在流体流动和弹性问题中，描述现象的方程的计算方法产生具有鞍点的数值系统；解决方案在一个局部看起来像马鞍的表面上。这类问题的计算方法有特殊的困难。会议讨论了处理大型数值系统、非线性、求解所需的时间和工作量、鞍点以及多处理器计算机的使用等方面的算法进展。

Manteuffel 9727525 The researcher and his colleagues organize a conference devoted to iterative methods for the solution of linear and nonlinear systems of equations. Particular themes are nonsymmetric linear systems, globally convergent algorithms for nonlinear systems, algorithms of optimal order of work, saddle point problems, and applications on multiprocessor computer architectures. The mathematical description of real-world problems leads inevitably to equations to solve. Many times the equations are nonlinear ones, arising because the underlying problem is nonlinear. Often, however, the original problem is linear and the mathematical equations are too. Such problems arise in all areas of science and technology, and are of special interest in biology, materials, environmental studies, and manufacturing. Progress in these areas requires solution of more comprehensive modeling equations --- such models are usually more nonlinear than simpler models ---, or more accurate solution of existing models --- increasing the size of the numerical problem to be solved. In certain problems, notably in fluid flow and in elasticity, computational methods for the equations describing the phenomena yield numerical systems having a saddle point; the solution is on a surface that looks locally like a saddle. Computational methods for such problems offer special difficulties. The conference addresses advances in algorithms to deal with larger numerical systems, nonlinearities, the amount of time and work needed to get a solution, saddle points, and the use of multiprocessor computers.