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In this paper, we propose methods to accelerate the solution of multiple related linear systems of equations. Such systems arise, for example, in building pattern libraries for interconnect parasitic extraction, parasitic extraction under process variation, and parameterized interconnect characterization. Our techniques include methods based on a generalized form of ldquorecycledrdquo Krylov subspace methods that use the sharing of information between related systems of equations to accelerate the iterative solution and methods to reuse computational effort during system matrix setup. Experimental results on electrostatic problems demonstrate significant improvement over existing methods that are based on solving each system individually. The proposed methods are generic, fully treat nonlinear perturbations without approximation and can potentially be applied to a wide variety of application domains outside electrostatic analysis.