A projection method of the cimmino type for linear algebraic systems

✍ Scribed by Fridrich Sloboda

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 283 KB
• Volume: 17
• Category: Article
• ISSN: 0167-8191
• DOI: 10.1016/s0167-8191(05)80146-2

✦ Synopsis

Sloboda, F. A projection method the Cimmino type for linear algebraic systems, Parallel Computing 17 (1991) 435-442.

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 ~ 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 T k-diagonally dominant matrix with k >1 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.