Condition number estimators in a sparse matrix software
SIAM Journal on Scientific and Statistical Computing
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Direct methods for sparse matrices
Direct methods for sparse matrices
The behavior of conjugate gradient algorithms on a multivector processor with a hierarchical memory
Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
ACM Transactions on Mathematical Software (TOMS)
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Finite element solution of boundary value problems: theory and computation
Finite element solution of boundary value problems: theory and computation
ICS '94 Proceedings of the 8th international conference on Supercomputing
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The problem of finding an approximation of @@@@ = A†b (where A† is the pseudo-inverse of A ∈ @@@@m@@@@n with m ≥ n and rank(A) = n) is discussed. It is assumed that A is sparse but has neither a special pattern (as bandedness) nor a special property (as symmetry or positive definiteness). In this paper it is shown that preconditioners obtained by neglecting small elements during the decomposition of A into easily invertible matrices can be used efficiently with conjugate gradient-type methods if an adaptive strategy for deciding when an element is small is implemented. The resulting preconditioned methods are often better than the corresponding direct and pure iterative methods or those based on preconditionings in which elements are neglected when they appear in a predefined set of positions in the matrix, i.e. positional rather than numerical dropping. Numerical results are given to illustrate the performance of the CG-type methods preconditioned via numerical dropping.