The use of a scientific, on-line database for function approximation is a technique that can significantly reduce the computational demands for problems requiring the frequent evaluation of computationally expensive functions. In this paper we present several new algorithms which significantly improve the performance of software implementations of this database approach. These algorithms are of two types-first, algorithms designed to improve the database retrieval rates; and, second, algorithms that seek to reduce the size of the database and subsequently reduce the cost of database queries. We have developed a software implementation of algorithms called DOLFA. We present experimental results which detail the performance of the DOLFA software for one representative combustion application. We observe significant improvements in cumulative time needed for database operations and memory requirements in a comparison of DOLFA to the function tabulation software system ISAT.