This book contains papers on sparse matrices and their appli cations which were presented at a Symposium held at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York on September 9-10, 1971. This is a very active field of research since efficient techniques for handling sparse matrix calculations are an important aspect of problem solving. In large scale problems, the feasibility of the calculation depends critically on the efficiency of the underlying sparse matrix algorithms. An important feature of the conference and its proceedings is the cross-fertilization achieved among a broad spectrum of application areas, and among combinatorialists, numerical analysts, and computer scientists. The mathematical, programming, and data management features of these techniques provide a unifying theme which can benefit readers in many fields. The introduction summarizes the major ideas in each paper. These ideas are interspersed with a brief survey of sparse matrix technology. An extensive unified bibliography is provided for the reader interested in more systematic information. The editors wish to thank Robert K. Brayton for his many helpful suggestions as chairman of the organizing committee and Redmond O'Brien for his editorial and audio-visual assistance. We would also like to thank Mrs. Tiyo Asai and Mrs. Joyce Otis for their help during the conference and on the numerous typing jobs for the manuscript. A special thanks goes to William J. Turner for establishing the IBM Research Symposia Series with Plenum Press.