Math libraries are an important part of programming environments that support the development of application software. While broadly available on sequential computers, math libraries are rare for parallel computers - especially in the case of distributed computing across networks of workstations. This project is to conduct research leading to a portable version of the LAPACK library for network distributed computers. LAPACK was selected since it is probably the most important math library in use today. The key research issues to resolve in this project are to find data decompositions and algorithms that support efficient execution with the coarse granularities found on networks of workstations. These results will be analyzed as part of the feasibility study. They will form the basis of the work plan for implementing the library for the Phase II proposal that would follow.