Parallel algorithms in computational linear algebra
Parallel computers and computations
Unitary Triangularization of a Nonsymmetric Matrix
Journal of the ACM (JACM)
Linear Least Squares by Elimination and MGS
Journal of the ACM (JACM)
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Pseudoinversus and conjugate gradients
Communications of the ACM
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A projection method of the Cimmino type for the minimum norm solution of a system of linear algebraic equations Ax = b, where A is an m x n matrix, m @? n and rank(A) = m and where b @e R(A) the range of A is described. The algorithm converges provided certain practical estimations of the dominance of AA^T hold. It is shown that @a = 1 is the optimal step-size choice for systems with AA^Tk-diagonally dominant matrix with k = 1. The algorithm in these cases converges fast also when A is not diagonally dominant. The algorithm, owing to its natural parallelism, is effectively implementable on vector computers such as CRAY-1 and CYBER 205 and on multiprocessors systems such as CRAY X-MP/48 and ALLIANT FX/80.