An efficient dual algorithm for vectorless power grid verification under linear current constraints
Proceedings of the 47th Design Automation Conference
Vectorless verification of RLC power grids with transient current constraints
Proceedings of the International Conference on Computer-Aided Design
A hierarchical matrix inversion algorithm for vectorless power grid verification
Proceedings of the International Conference on Computer-Aided Design
Deterministic random walk preconditioning for power grid analysis
Proceedings of the International Conference on Computer-Aided Design
Parallel forward and back substitution for efficient power grid simulation
Proceedings of the International Conference on Computer-Aided Design
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This paper presents a new stochastic preconditioning approach for large sparse matrices. For the class of matrices that are rowwise and columnwise irreducibly diagonally dominant, we prove that an incomplete $\rm{LDL^T}$ factorization in a symmetric case or an incomplete LDU factorization in an asymmetric case can be obtained from random walks and used as a preconditioner. It is argued that our factor matrices have better quality, i.e., better accuracy-size trade-offs, than preconditioners produced by existing incomplete factorization methods. Therefore a resulting preconditioned Krylov-subspace iterative solver requires less computation than traditional methods to solve a set of linear equations with the same error tolerance. The advantage increases for larger and denser matrices. These claims are verified by numerical tests, and we provide techniques that can potentially extend the theory to non-diagonally-dominant matrices.