This is a Minority Research Initiation (MRI) Planning Grant proposal in computational theory to develop 1) numerical techniques for parallel processing and 2) application of computing machinery and methods to large systems problems. The overall goal is to integrate the two areas. During the planning period the investigator will develop effective ordering procedures for the applications of parallel sparse vector methods such as, parallel triangulation and inversion of matrices. Feasibility studies of these methods and testing them on an actual supercomputer system will be conducted. This grant will provide support for a well-trained minority scientist to perform these and other preliminary activities as a basis for developing a competitive proposal for submission to the MRI research initiation component.