### Recycling Krylov Subspaces for Solving Linear Systems with Successively Changing Right-hand Sides Arising in Model Reduction [chapter]

Peter Benner, Lihong Feng
2011 Lecture Notes in Electrical Engineering
We discuss the numerical solution of successive linear systems of equations Ax = b i , i = 1, 2, . . . m, by iterative methods based on recycling Krylov subspaces. We propose various recycling algorithms which are based on the generalized conjugate residual (GCR) method. The recycling algorithms reuse the descent vectors computed while solving the previous linear systems Ax = b j , j = 1, 2, . . . , i − 1, such that a lot of computational work can be saved when solving the current system Ax = b
more » ... rrent system Ax = b i . The proposed algorithms are robust for solving sequences of linear systems arising in circuit simulation. Sequences of linear systems need to be solved, e.g., in model order reduction (MOR) for systems with many terminals. Numerical experiments illustrate the efficiency and robustness of the proposed method.