We provide eigenvalue intervals for symmetric saddle-point and regularised saddle-point matrices in the case where the (1,1) block may be indefinite. These generalise known results for the definite (1,1) case. We also study the spectral properties of the equivalent augmented formulation, which is an alternative to explicitly dealing with the indefinite (1,1) block. Such an analysis may be used to assess the convergence of suitable Krylov subspace methods. We conclude with spectral analyses of the effects of common block-diagonal preconditioners.
N. Gould, V. Simoncini (2009). Spectral Analysis of saddle point matrices with indefinite leading blocks. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 31, 1152-1171 [10.1137/080733413].
Spectral Analysis of saddle point matrices with indefinite leading blocks
SIMONCINI, VALERIA
2009
Abstract
We provide eigenvalue intervals for symmetric saddle-point and regularised saddle-point matrices in the case where the (1,1) block may be indefinite. These generalise known results for the definite (1,1) case. We also study the spectral properties of the equivalent augmented formulation, which is an alternative to explicitly dealing with the indefinite (1,1) block. Such an analysis may be used to assess the convergence of suitable Krylov subspace methods. We conclude with spectral analyses of the effects of common block-diagonal preconditioners.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.