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On the Approximate Cyclic Reduction Preconditioner
 SIAM J. Sci. Comput
, 2000
"... We present a preconditioning method for the iterative solution of large sparse systems of equations. The preconditioner is based on ideas both from ILU preconditioning and from multigrid. The resulting preconditioning technique requires the matrix only. A multilevel structure is obtained by using ma ..."
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Cited by 16 (3 self)
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We present a preconditioning method for the iterative solution of large sparse systems of equations. The preconditioner is based on ideas both from ILU preconditioning and from multigrid. The resulting preconditioning technique requires the matrix only. A multilevel structure is obtained by using maximal independent sets for graph coarsening. A Schur complement approximation is constructed using a sequence of point Gaussian elimination steps. The resulting preconditioner has a transparant modular structure similar to the algoritmic structure of a multigrid Vcycle.
An Algebraic Multilevel Preconditioner for Symmetric Positive Definite and Indefinite Problems
 Numerical Challenges in Lattice Quantum Chromodynamics, Lecture Notes in Computational Science and Engineering
"... We present a preconditioning method for the iterative solution of large sparse systems of equations. The preconditioner is based on ideas both from ILU preconditioning and from multigrid. The resulting preconditioning technique requires the matrix only. A multilevel structure is obtained by construc ..."
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Cited by 2 (0 self)
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We present a preconditioning method for the iterative solution of large sparse systems of equations. The preconditioner is based on ideas both from ILU preconditioning and from multigrid. The resulting preconditioning technique requires the matrix only. A multilevel structure is obtained by constructing a maximal independent set of the graph of a reduced matrix. The computation of a Schur complement approximation is based on a Galerkin approach with a matrix dependent prolongation and restriction. The resulting preconditioner has a transparant modular structure similar to the algorithmic structure of a multigrid Vcycle. The method is applied to symmetric positive definite and indefinite Helmholtz problems. The multilevel preconditioner is compared with standard ILU preconditioning methods.
Optimal Folding Of Standard And Custom Cells
 ACM Transactions on Design Automation of Electronic Systems
, 1996
"... We study the problem of folding an ordered list of standard and custom cells into rows of a chip so as to minimize either the routing area or the total chip area. Nine versions of the folding problem are formulated and fast polynomail time algorithms are obtained for each. Two of our formulations ..."
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Cited by 1 (1 self)
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We study the problem of folding an ordered list of standard and custom cells into rows of a chip so as to minimize either the routing area or the total chip area. Nine versions of the folding problem are formulated and fast polynomail time algorithms are obtained for each. Two of our formulations correspond to problems formulated in [PAIK93] for the folding of a stack of bitslice components. Our algorithms for these two formulations are asymptotically superior to those of [PAIK93].
Construction of Combinatorial Objects
, 1995
"... Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, u ..."
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Cited by 1 (1 self)
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Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, using an algorithmic version of Burnside's table of marks, computing double coset representatives, and computing Sylow subgroups of automorphism groups can be explained in this way. The exposition is based on graph theoretic concepts to give an easy explanation of data structures for group actions.