Efficient Data Structures and Algorithms for Scientific Computations.

Large-scale numerically intensive scientific applications can require tremendous amounts of computer time and space. Two general methods are presented for reducing the computer resources required in scientific computing. The first is a numerical database system which is built on a space and time optimal data structure called a weighted search tree and that allows for the storage and retrieval of valuable intermediate information so costly redundant calculations can be avoided. The second is a matrix algorithm based on a new space optimal representation of sparse matrices that for typical scientific applications can be expected to dramatically decrease the cost of multiplying sparse matrices. Codes and tests for each are given. Both methods can be implemented in a broad range of large-scale scientific applications