Eigenvalue bounds for double saddle-point systems
Susanne Bradley, Chen Greif
Abstract
Abstract We derive bounds on the eigenvalues of a generic form of double saddle-point matrices. The bounds are expressed in terms of extremal eigenvalues and singular values of the associated block matrices. Inertia and algebraic multiplicity of eigenvalues are considered as well. The analysis includes bounds for preconditioned matrices based on block diagonal preconditioners using Schur complements, and it is shown that in this case the eigenvalues are clustered within a few intervals bounded away from zero. Analysis for approximations of Schur complements is included. Some numerical experiments validate our analytical findings.
Topics & Concepts
MathematicsEigenvalues and eigenvectorsSaddle pointSaddleDiagonalMultiplicity (mathematics)Algebraic numberBounded functionMathematical analysisApplied mathematicsPure mathematicsGeometryMathematical optimizationPhysicsQuantum mechanicsMatrix Theory and AlgorithmsElectromagnetic Scattering and AnalysisAdvanced Numerical Methods in Computational Mathematics