Random projection preserves stability with high probability

抄録

In a projection-based model reduction, a Galerkin-type projection is frequently used to generate a reduced matrix. However, the stability may not be preserved and the computational effort for generating the projection is not negligible. In this study, we use random projections to reduce an original large-scale matrix. We show that the stability of the reduced matrix is guaranteed with high probability and that the matrix can be obtained efficiently.