Showing papers on "Sparse approximation published in 1969"

Projection Methods for Solving Sparse Linear Systems

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.

Sparse matrix techniques in two mathematical programming codes

Abstract: : The authors empirically compared ten pivot selection rules for representing the inverse of a sparse basis in triangularized product form. On examples drawn from actual applications, one of the rules yield inverses that were only slightly less sparse than the original basis. The rule was used in the M5 mathematical programming system and has resulted in substantial reduction in running time.