A survey of sparse matrix research

This paper surveys the state of the art in sparse matrix research in January 1976. Much of the survey deals with the solution of sparse simultaneous linear equations, including the storage of such matrices and the effect of paging on sparse matrix algorithms. In the symmetric case, relevant terms from graph theory are defined. Band systems and matrices arising from the discretization of partial differential equations are treated as separate cases. Preordering techniques are surveyed with particular emphasis on partitioning (to block triangular form) and tearing (to bordered block triangular form). Methods for solving the least squares problem and for sparse linear programming are also reviewed. The sparse eigenproblem is discussed with particular reference to some fairly recent iterative methods. There is a short discussion of general iterative techniques, and reference is made to good standard texts in this field. Design considerations when implementing sparse matrix algorithms are examined and finally comments are made concerning the availability of codes in this area.