A sparse matrix is defined to be a matrix containing a high proportion of elements that are zeros. Sparse matrices of large order are of great interest and application in science and industry; for example, electrical networks, structural engineering, power distribution, reactor diffusion, and solutions to differential equations While conclusions within this paper are primarily drawn considering orders of greater than 1000, much ~s applicable to sparse matrices of smaller orders in the hundreds.

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... Because of increasing use of large order sparse matrices and the tendency to attempt to solve larger order problems, great attention must be focused on core storage and execution time Every effort should be made to optimize both computer memory allocation and executmn times, as these are the limiting factors that most often dictate the practicahty of solving a given problem Indexing algorithms are the subject of this paper, as they are generMly recognized as the most ~mportant factor in fast and efficient processing of large order sparse matrices. Indexing schemes of main interest are the bit map, address map, row-column, and the threaded list Major variations of the indexing techniques above mentioned are noted, as well as the particular indexing scheme inherent in diagonal or band matrices. The concluding section of the paper compares the types of methods, discusses their suitabihty for different types of processing, and makes suggestions eoneernlng the adaptability and flexibility of the maj or exmting methods of indexing algorithms for application to user problems