Element-by-Element Schur Complement Approximations for General Nonsymmetric Matrices of Two-by-Two Block Form

Authors: Neytcheva, M., He, X., Do-Quang, M.
Document Type: Article
Pubstate: Published
Journal: Lecture Notes in Computer Science
Volume: 5910   108
Year: 2010


We consider element-by-element Schur complement approximations for indefinite and general nonsymmetric matrices of two-by-two block form, as arising in finite element discretized systems of PDEs. The paper provides some analysis of the so-obtained approximation and attempts to quantify the quality of the underlying two-by-two matrix splitting in a way similar to that used for symmetric positive definite matrices. The quality of the approximation is illustrated numerically.