Numerical data bases arise in many scientific applications to keep track of large sparse and dense matrices. Unlike the many matrix data storage techniques available for Incore manipulation, very large matrices are currently limited to a few compact storage schemes on secondary devices, due to the complex underlying data management facilities. This paper proposes an approach for generalized numerical database management that would promote physical data independence by relieving users from the need for knowledge of the physical data organization on the secondary devices. Our approach is to describe each of the storage techniques for dense and sparse matrices by a physical schema, which encompasses the corresponding access path, the encoding to storage structures, and the file access method. A generalized facility for describing any kind of numerical database and its mapping to storage is provided via nonprocedural Stored-Data Description and Mapping Languages (SDDL and SDML). The languages are processed by a Generalized Syntax-Directed Translation Scheme (GSDTS) to automatically generate FORTRAN conversion programs for creating or translating numerical database from one compact storage scheme to another. The feasibility of the generalized approach with regard to our current implementation is also discussed.