Projection Methods for Solving Sparse Linear Systems

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Abstract
Some methods of successive approximation for the solution of simultaneous linear equations are discussed. The coefficient matrix A of the linear system is assumed to be sparse. It is shown that savings in the computer storage and the computing time are possible, if there exists a subset of the rows (columns) of A, consisting of only orthogonal rows (columns). Such savings are also possible, if for some permutation matrices P and Q, PAQ has a particular structure, viz., singly bordered block diagonal form. It is shown that the set of orthogonal rows (columns) of A, as well as P and Q can be determined by using some results from graph theory (e.g., incidence matrices, row and column graphs, points of attachment). Geometrical interpretations of the methods and their inter-relatiohip are given.

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