Computer algorithms for solving linear algebraic equations : the state of the art

This volume presents the lectures given by fourteen specialists in algorithms for linear algebraic systems during a NATO Advanced Study Institute held at Il Ciocco, Barga, Italy, September 1990. Topics related to sequential formulation include: a review of classical methods with some new proofs; presentations of complexity results; algorithms for linear least squares; ABS methods; multigrid methods; preconditioned conjugate gradient methods for H-matrices; domain decomposition methods; hierarchical basis methods and; splitting type methods. With reference to implementations on multiprocessors, topics include algorithms for general sparse systems, factorization methods for dense matrices, Gaussian elimination on systolic arrays, and methods for linear systems arising in optimization problems. The book may serve as a useful introduction to a field still in rapid growth and as a reference to recent results in the field.