Sparse matrices in astronomical data reduction

Abstract

Sparse matrices occur frequently in astronomical data adjustment problems. Use of special techniques that take advantage of the sparcity structure can result in substantial saving of computer memory and execution time. In astrometry, for example, when one uses minor planets, or other objects, to determine parameters common to all of the observations, memory and execution time are saved by storing only the nonzero elements of the matrix in a vector and deriving an index function to locate them uniquely. Although the indexing of elements and the solution of the linear system become complicated, the saving of memory compared with an upper triangular matrix is 1-36p(p−1)/n(n+1), where p is the number of minor planets and n the number of unknowns