Explicit approximate inverse preconditioning techniques
ABSTRACT The numerical treatment and the production of related software for solving large sparse linear systems of algebraic equations,
derived mainly from the discretization of partial differential equation, by preconditioning techniques has attracted the attention
of many researchers. In this paper we give an overview of explicit approximate inverse matrix techniques for computing explicitly
various families of approximate inverses based on Choleski and LU—type approximate factorization procedures for solving sparse
linear systems, which are derived from the finite difference, finite element and the domain decomposition discretization of
elliptic and parabolic partial differential equations. Composite iterative schemes, using inner-outer schemes in conjunction
with Picard and Newton method, based on approximate inverse matrix techniques for solving non-linear boundary value problems,
are presented. Additionally, isomorphic iterative methods are introduced for the efficient solution of non-linear systems.
Explicit preconditioned conjugate gradient—type schemes in conjunction with approximate inverse matrix techniques are presented
for the efficient solution of linear and non-linear system of algebraic equations. Theoretical estimates on the rate of convergence
and computational complexity of the explicit preconditioned conjugate gradient method are also presented. Applications of
the proposed methods on characteristic linear and non-linear problems are discussed and numerical results are given.
Article: Performance analysis of an electrical substation via Semi Markov process computed by generalized approximate inverse preconditioning[show abstract] [hide abstract]
ABSTRACT: An electrical substation is simulated by a Semi Markov process model and a performability indicator was computed in order to estimate asymptotically the amount of the mean energy not supplied due to different maintenance policies. Additionally, the same study was performed by a Homogeneous Markov process in order to compare the results. Moreover, the steady state probabilities were computed by solving a sparse linear system of algebraic equations, using generalized explicit approximate inverse preconditioning methods.
Conference Proceeding: On the performance of parallel normalized explicit preconditioned conjugate gradient type methods.20th International Parallel and Distributed Processing Symposium (IPDPS 2006), Proceedings, 25-29 April 2006, Rhodes Island, Greece; 01/2006